Updated on 2026/04/21
「ある制約条件を満たす集合の中から最良のものを見つけ出す」という最適化を数学的アプローチで行う、数理最適化の分野を専門にしています。
特に、量子化学や組合せ最適化など幅広く利用されている半正定値計画問題を中核として、理論的研究からソフトウェアへの実装など研究しています。
最近では、半正定値計画問題で培った基礎研究を活用して、樹木園における種別構成問題や医療における最適化問題にも取り組んでいます。
Parallel Computing for Large-scale Semidefinite Programs
2013/02/28
Languages： English
Doctor of Science ( 2004.3 Tokyo Institute of Technology )
Mathematical Optimization
Mathematical Optimization
Semidefinite Programs
Continuous Optimization
Conic Optimization
Natural Science / Basic mathematics
Social Infrastructure (Civil Engineering, Architecture, Disaster Prevention) / Social systems engineering
Informatics / Mathematical informatics
Natural Science / Applied mathematics and statistics
Tokyo Institute of Technology Information Science and Engineering Mathematical and Computing Sciences
- 2004.3
Country： Japan
Tokyo Institute of Technology Graduate School of Information Science and Engineering Department of Mathematical and Computing Sciences
- 2004
Institute of Science Tokyo Department of Mathematical and Computing Science Professor
2024.10
Tokyo Institute of Technology Department of Mathematical and Computing Science Professor
2020.9 - 2024.9
Tokyo Institute of Technology Department of Mathematical and Computing Science Associate Professor
2016.4 - 2020.8
-:東京工業大学 情報理工学研究科 数理・計算科学専攻 准教授
2012.10 - 2016.3
-:東京工業大学 情報理工学研究科 数理・計算科学専攻 助教
2008.4 - 2012.9
:神奈川大学 工学部情報システム創成学科 特別助教
2007.4 - 2008.3
:神奈川大学 工学部情報システム創成学科 特別助手
2004.4 - 2007.3
日本オペレーションズ・リサーチ学会
INFORMS (Informatics on Operations Research and Management Science)
日本経営工学会
Mathematical Optimization Society
SIAM (Society for Industrial and Applied Mathematics)
日本オペレーションズ・リサーチ学会 研究理事
2021.5 - 2023.5
Committee type：Academic society
日本経営工学会 代議員
2019.6
Committee type：Academic society
日本経営工学会 支部委員
2017.6
Committee type：Academic society
日本経営工学会 関東支部事務局長
2017.6 - 2021.6
Committee type：Academic society
日本経営工学会 代議員
2015.5 - 2017.5
Committee type：Academic society
ICCOPT (International Conference on Continuous Optimization) 2016 Tokyo 実行委員
2013 - 2016
Committee type：Academic society
日本オペレーションズ・リサーチ学会 庶務幹事
2010.4 - 2013.3
Committee type：Academic society
日本オペレーションズ・リサーチ学会 第20回RAMPシンポジウム実行委員
2008
Committee type：Academic society
日本経営工学会 西関東支部運営委員
2007.6 - 2017.6
Committee type：Academic society
An inexact infeasible arc-search interior-point method for linear optimization problems Reviewed International coauthorship International journal
Einosuke Iida, Makoto Yamashita
Numerical Algorithms 2026.4
A difference-of-convex approach for log-determinant semidefinite programming with chordal sparsity Reviewed International coauthorship International journal
Ryoga Masaki, Xiangyu Yang, Makoto Yamashita
Numerical Algorithms 2026.3
Verifying Robustness of Neural Networks with Tight Semidefinite Relaxations Reviewed International coauthorship International journal
Godai Azuma, Sunyoung Kim, Makoto Yamashita
Computational Optimization and Applications 2026.2
Optimizing Cooperative Carrier-Vehicle Routing with Iterative Second-Order Cone Programming Method Reviewed International coauthorship International journal
Ning-Wen Yang, Maharani Rizki Larasati, I-Lin Wang, Makoto Yamashita
Annals of Operations Research 2026.2
Dual spectral projected gradient method for generalized log-det semidefinite programming Reviewed International coauthorship International journal
Charles Namchaisiri, Makoto Yamashita
Optimization Methods and Software 40 ( 6 ) 1454 - 1472 2025.9
A new dual spectral projected gradient method for log-determinant semidefinite programming with hidden clustering structures Reviewed International coauthorship International journal
Charles Namchaisiri, Tianxiang Liu, Makoto Yamashita
Computational Optimization and Applications 92 ( 2 ) 589 - 615 2025.6
Rank-one matrix completion via high-rank matrices in sum-of-squares relaxations Reviewed International coauthorship International journal
Godai Azuma, Sunyoung Kim, Makoto Yamashita
Journal of Global Optimization 92 ( 2 ) 321 - 343 2025.3
T-semidefinite programming relaxation with third-order tensors for constrained polynomial optimization Reviewed International coauthorship International journal
Hiroki Marumo, Sunyoung Kim, Makoto Yamashita
Computational Optimization and Applications 89 ( 1 ) 183 - 218 2024.6
An infeasible interior-point arc-search method with Nesterov’s restarting strategy for linear programming problems Reviewed International coauthorship International journal
Einosuke Iida, Makoto Yamashita
Computational Optimization and Applications 88 ( 2 ) 643 - 676 2024.2
Masaaki Tamai, Makoto Yamashita
Optimization 1 - 39 2024
Projection Onto Convex Sets Approach to Solve Homogeneous Self Dual Model of Portfolio Optimization Reviewed
Subchan Subchan, Makoto Yamashita, Alvian Alif Hidayatullah, Sena Safarina, Mahmud Yunus
2023 International Conference on Advanced Mechatronics, Intelligent Manufacture and Industrial Automation (ICAMIMIA) 667 - 672 2023.11
Exact SDP relaxations for quadratic programs with bipartite graph structures Reviewed
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
Journal of Global Optimization 86 671 - 691 2023
Exploiting aggregate sparsity in second-order cone relaxations for quadratic constrained quadratic programming problems Reviewed
Heejune Sheen, Makoto Yamashita
OPTIMIZATION METHODS & SOFTWARE 2022.9
Exact SDP relaxations of quadratically constrained quadratic programs with forest structures Reviewed
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
Journal of Global Optimization 82 ( 2 ) 243 - 262 2021.9
An infeasible interior-point arc-search algorithm for nonlinear constrained optimization Reviewed
Makoto Yamashita, Einosuke Iida, Yaguang Yang
Numerical Algorithms 89 ( 1 ) 249 - 275 2021.5
Shugo Miyamoto, Makoto Yamashita
SN Applied Sciences 3 ( 2 ) 2021.2
A dual spectral projected gradient method for log-determinant semidefinite problems Reviewed
Takashi Nakagaki, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
Computational Optimization and Applications 76 ( 1 ) 33 - 68 2020.5
Conic relaxation approaches for equal deployment problems Reviewed
Sena Safarina, Tim J. Mullin, Satoko Moriguchi, Makoto Yamashita
Discrete Applied Mathematics 275 111 - 125 2020.3
On the conditions for the finite termination of ADMM and its applications to SOS polynomials feasibility problems Reviewed
Hikaru Komeiji, Sunyoung Kim, Makoto Yamashita
Computational Optimization and Applications 74 ( 2 ) 317 - 344 2019.11
育種学に表れる種別構成問題に対する短時間数値解法の構築 Invited
山下真, Sena Safaina, Tim J. Mullin, 森口聡子
数理科学 57 ( 11 ) 58 - 65 2019.11
Polyhedral-based Methods for Mixed-Integer SOCP in Tree Breeding Reviewed
Sena Safarina, Tim J. Mullin, Makoto Yamashita
Journal of the Operations Research Society of Japan 62 ( 4 ) 133 - 151 2019.11
Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods Reviewed
Masaki Kimizuka, Sunyoung Kim, Makoto Yamashita
Journal of Global Optimization 75 ( 3 ) 631 - 654 2019.11
A Cone Decomposition Method for Optimal Contribution Selection in Forest Tree Management
Sena Safarina, Tim J. Mullin, Makoto Yamashita
2018 14 - 21 2019.4
Non-monotone Spectral Projected Gradient Method for Semidefinite Program with Log-Determinant and ℓ_1-Norm Terms
2108 22 - 30 2019.4
東京工業大学情報理工学院数理・計算科学系―情報の未来を作り出す数理的アプローチを探究する―
金森敬文, 樺島祥介, 高安美佐子, 中野 張, 福田光浩, 三好直人, 山下 真, 渡邊澄夫
オペレーションズ・リサーチ 2019.1
An arc-search O(nL) infeasible-interior-point algorithm for linear programming Reviewed
Yaguang Yang, Makoto Yamashita
Optimization Letters 12 ( 4 ) 781 - 798 2018.6
A successive LP approach with C-VaR type constraints for IMRT optimization Reviewed
Shogo Kishimoto, Makoto Yamashita
Operations Research for Health Care 17 55 - 64 2018.6
An efficient second-order cone programming approach for optimal selection in tree breeding Reviewed
Makoto Yamashita, Tim J. Mullin, Sena Safarina
Optimization Letters 12 ( 7 ) 1 - 15 2018.1
Fast implementation for semidefinite programs with positive matrix completion Reviewed
Makoto Yamashita, Kazuhide Nakata
OPTIMIZATION METHODS & SOFTWARE 30 ( 5 ) 1030 - 1049 2015.10
Using semidefinite programming to optimize unequal deployment of genotypes to a clonal seed orchard Reviewed
J. Ahlinder, T. J. Mullin, M. Yamashita
TREE GENETICS & GENOMES 10 ( 1 ) 27 - 34 2014.2
Tomohiko Mizutani, Makoto Yamashita
JOURNAL OF GLOBAL OPTIMIZATION 56 ( 3 ) 1073 - 1100 2013.7
Masakazu Kojima, Makoto Yamashita
MATHEMATICAL PROGRAMMING 138 ( 1-2 ) 333 - 364 2013.4
The second-order reduced density matrix method and the two-dimensional Hubbard model Reviewed
James S.M. Anderson, Maho Nakata, Ryo Igarashi, Katsuki Fujisawa, Makoto Yamashita
Computational and Theoretical Chemistry 1003 22 - 27 2013.1
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 39 ( 1 ) 2012.11
Sunyoung Kim, Masakazu Kojima, Hayato Waki, Makato Yamashita
ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 38 ( 4 ) 2012.8
High-Performance General Solver for Extremely Large-Scale Semidefinite Programming Problems Reviewed
Katsuki Fujisawa, Toshio Endo, Hitoshi Sato, Makoto Yamashita, Satoshi Matsuoka, Maho Nakata
2012 INTERNATIONAL CONFERENCE FOR HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS (SC) 93 2012
Sunyoung Kim, Masakazu Kojima, Martin Mevissen, Makoto Yamashita
MATHEMATICAL PROGRAMMING 129 ( 1 ) 33 - 68 2011.9
CONSTRUCTING POLYHEDRAL HOMOTOPIES ON GRID-OF-CLUSTERS Reviewed
Tomohiko Mizutani, Makoto Yamashita
PACIFIC JOURNAL OF OPTIMIZATION 7 ( 2 ) 369 - 386 2011.5
Efficient parallel software for large-scale SemiDefinite Programs Reviewed
Makoto Yamashita, Katsuki Fujisawa
Proceedings of the IEEE International Symposium on Computer-Aided Control System Design 1 - 6 2010
Variational calculation of second-order reduced density matrices by strong N-representability conditions and an accurate semidefinite programming solver Reviewed
Maho Nakata, Bastiaan J. Braams, Katsuki Fujisawa, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao
JOURNAL OF CHEMICAL PHYSICS 128 ( 16 ) 164113 2008.4
Optimization Software SDPA Reviewed
Nakata Kazuhide, Fujisawa Katsuki, Fukuda Mituhiro, Yamashita Makoto, Nakata Maho, Kobayashi Kazuhiro
Bulletin of the Japan Society for Industrial and Applied Mathematics 18 ( 1 ) 2 - 14 2008
SDPA project: solving large-scale semidefinite programs Reviewed
Katsuki Fujisawa, Kazuhide Nakata, Makoto Yamashita, Mituhiro Fukuda
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN 50 ( 4 ) 278 - 298 2007.12
Large-scale semidefinite programs in electronic structure calculation Reviewed
Mituhiro Fukuda, Bastiaan J. Braams, Maho Nakata, Michael L. Overton, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao
MATHEMATICAL PROGRAMMING 109 ( 2-3 ) 553 - 580 2007.3
Parallel Solver for SemiDefinite Programming Reviewed
Makoto Yamashita, Katsuki Fujisawa, Kazuhide Nakata
International Journal of Logistics and SCM systems 2 ( 1 ) 22 - 29 2007
SEMIDEFINITE PROGRAMMING: FORMULATIONS AND PRIMAL-DUAL INTERIOR-POINT METHODS
Mituhiro Fukuda, Maho Nakata, Makoto Yamashita
REDUCED-DENSITY-MATRIX MECHANICS - WITH APPLICATION TO MANY-ELECTRON ATOMS AND MOLECULES 134 103 - 118 2007
Simple Hamiltonians which exhibit drastic failures by variational determination of the two-particle reduced density matrix with some well known N-representability conditions Reviewed
Maho Nakata, Bastiaan J. Braams, Mituhiro Fukuda, Jerome K. Percus, Makoto Yamashita, Zhengji Zhao
JOURNAL OF CHEMICAL PHYSICS 125 ( 24 ) 244109 2006.12
Parallel Primal-Dual Interior-Point Methods for SemiDefinite Programs
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata
Parallel Combinatorial Optimization 211 - 238 2006.4
A parallel primal-dual interior-point method for semidefinite programs using positive definite matrix completion Reviewed
K Nakata, M Yamashita, K Fujisawa, M Kojima
PARALLEL COMPUTING 32 ( 1 ) 24 - 43 2006.1
Solving large scale optimization problems via grid and cluster computing Reviewed
K Fujisawa, M Kojima, A Takeda, M Yamashita
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN 47 ( 4 ) 265 - 274 2004.12
High performance grid and cluster computing for some optimization problems Reviewed
K Fujisawa, M Kojima, A Takeda, M Yamashita
2004 INTERNATIONAL SYMPOSIUM ON APPLICATIONS AND THE INTERNET WORKSHOPS, PROCEEDINGS 612 - 615 2004
Second order cone programming relaxation of a positive semidefinite constraint Reviewed
S Kim, M Kojima, M Yamashita
OPTIMIZATION METHODS & SOFTWARE 18 ( 5 ) 535 - 541 2003.10
SDPARA: SemiDefinite Programming Algorithm paRAllel version Reviewed
M Yamashita, K Fujisawa, M Kojima
PARALLEL COMPUTING 29 ( 8 ) 1053 - 1067 2003.8
Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0) Reviewed
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima
Optimization Methods and Software 18 ( 4 II ) 491 - 505 2003.8
世界標準 MIT 教科書 ストラング：計算理工学
（ Role： Joint translator第８章「最適化と最小原理」の翻訳を担当）
近代科学社 2017.1
An Application of Polyhedral Relaxations to Optimal Contribution Selection of Tree Breeding Problem
Sena Safarina, Makoto Yamashita
RIMS Kokyuroku ( 2069 ) 62 - 73 2018.7
Conic relaxation approaches for equal deployment problems
Research reports on mathematical and computing sciences. Ser. B, Operations research 485 1 - 28 2017.3
国際会議 ICCOPT 2016 Tokyo 開催の経験と教訓 (5) -- プロポーザル作成・会計・アルバイト担当 Invited
福田光浩, 山下 真, 水谷 友彦
オペレーションズ・リサーチ 62 ( 10 ) 253 - 256 2017
救急車再配置問題に対する遺伝的プログラミングを用いた効果的手法の設計
山下 真
オペレーションズ・リサーチ 61 ( 10 ) 644 - 645 2016
2-F-3 対数行列式半正定値計画問題に対する双対スペクトラル射影勾配法の構築(連続最適化(3))
山下 真, 福田 光浩, 中垣 敬
日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集 2014 238 - 239 2014.3
半正定値計画問題に対する行列補完理論の高速実装 Invited
山下 真
オペレーションズ・リサーチ 59 ( 3 ) 138 - 144 2014
凹費用関数をもつ輸送問題に対する2乗和多項式緩和 (最適化手法の理論と応用の繋がり)
水谷 友彦, 山下 真
数理解析研究所講究録 1829 102 - 112 2013.3
Parallel Computing for Large-scale Semidefinite Programs
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
Tokyo Institute of Technology Bulletin 2013.2
2-C-10 センサーネットワークモデルにおける重み付けによる数値精度向上について(連続最適化(2))
金城 憲長, 山下 真, 福田 光浩, 下平 英寿
日本オペレーションズ・リサーチ学会秋季研究発表会アブストラクト集 2012 196 - 197 2012.9
Latest developments in the SDPA family for solving large-scale SDPs
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
International Series in Operations Research and Management Science 166 687 - 713 2012
2-D-6 凹費用関数をもつ輸送問題に対する半正定値計画緩和(最適化)
水谷 友彦, 山下 真
日本オペレーションズ・リサーチ学会秋季研究発表会アブストラクト集 2011 256 - 257 2011.9
主双対内点法に対する高速化・並列化の技術 Invited
山下 真
オペレーションズ・リサーチ 55 ( 7 ) 400 - 405 2010
2-G-2 重み付き対数行列式を持つ半正定値計画問題を解くSDPA(連続最適化(1))
福田 光浩, 中田 和秀, 藤澤 克樹, 山下 真
日本オペレーションズ・リサーチ学会秋季研究発表会アブストラクト集 2009 259 - 260 2009.9
Fujisawa Katsuki, Kojima Masakazu, Nakata Kazuhide, Fukuda Mituhiro, Yamashita Makoto, Nakata Maho
RIMS Kokyuroku 1614 ( 1614 ) 136 - 143 2008.10
2-D-14 最適化問題用オンライン・ソルバーの構築と自動選択機能の開発(非線形計画(3))
藤澤 克樹, 山下 真, 中田 和秀, 後藤 和茂
日本オペレーションズ・リサーチ学会秋季研究発表会アブストラクト集 2008 256 - 257 2008.9
2-D-6 半正定値計画による分子の電子構造計算(数理計画(1))
福田 光浩, 中田 真秀, BRAAMS Bastiaan J., 藤澤 克樹, PERCUS Jerome K., 山下 真, ZHAO Zhengji
日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集 2008 174 - 175 2008.3
Computational Prospects on Copositive Programming(Theory of Modeling and Optimization)
Fukuda Mituhiro, Yamashita Makoto, Kojima Masakazu
RIMS Kokyuroku 1526 207 - 213 2006.12
19th International Symposium on Mathematical Programming Invited
山下 真
応用数理 16 ( 4 ) 346 - 347 2006
Fukuda Mituhiro, Braams Bastiaan J., Nagata Maho[他], Overton Michael L., Percus Jerome K., Yamashita Makoto, Zhao Zhengji
RIMS Kokyuroku 1461 15 - 29 2005.12
平成17年度春季研究発表会ルポ Invited
山下 真, 中田 和秀, 後藤 順哉, 井床 利生
オペレーションズ・リサーチ 50 ( 7 ) 500 - 504 2005
半正定値計画に対する行列補完型主双対内点法の並列化(錘計画問題と相補正問題)
中田 和秀, 山下 真, 藤沢 克樹, 小島 政和
日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集 2004 10 - 11 2004.3
半正定値計画問題を解くソフトウェアのPCクラスタ上における並列実装(最適化(2))
山下 真, 藤沢 克樹, 小島 政和
日本オペレーションズ・リサーチ学会春季研究発表会アブストラクト集 2003 128 - 129 2003.3
正確なランク1行列補完のための二乗和緩和の疎性構造 Invited
東悟大, Sunyoung Kim, 山下真
シンポジウム：錐線形計画とその周辺 2024.2
An infeasible interior-point arc-search algorithm for nonlinear constrained optimization
Einosuke Iida, Makoto Yamashita, Yaguang Yang
10th International Congress on Industrial and Applied Mathematics 2023.8
Tightness conditions of SDP relaxation for QCQPs with bipartite graph structure
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
10th International Congress on Industrial and Applied Mathematics 2023.8
制約充足ソルバーを用いた手術スケジュール作成
黒田航太朗, 山下真, 乾文良,Malik, Olivier Boussejra, 志賀卓弥
日本オペレーションズ・リサーチ学会 2019年秋季研究発表会 2019.9
二部グラフで表現可能な疎性を持つ二次制約付き二次計画問題と狭小な半正定値計画緩和の条件
東悟大, 福田光浩, Kim Sunyoung, 山下真
日本オペレーションズ・リサーチ学会2022春季研究発表会 2022.3
Quantum Annealing for Balance Optimization Subset Selection Invited
Makoto Yamashita, Pornnapas Huntrakool
The International Conference on Mathematics: Pure, Applied, and Computation (ICoMPAC) 2021 2021.10
Exact semidefinite relaxations for QCQPs with forest-structured matrices and its applications
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
IFORS 2021 2021.8
緩和法とペナルティ法を用いた二次錐計画問題に対する安定した解法の構築
坂井祐太, 山下真
日本経営工学会関東支部2021年度学生論文発表会 2022.3
Bilevel Nonsmooth Optimization for l2,q-hyperparameter Selection
2022.3
A Cone Decomposition Method for Semi-Integer Problems
Sena Safarina, Makoto Yamashita
SIAM Conference on Optimization 2021 2021.7
角度情報付きセンサーネットワーク位置推定問題に対するブロック座標降下法の提案
浅野有紀, 山下真
日本経営工学会関東支部2020年度学生論文発表会 2021.3
Efficient SOCP Relaxations for Pooling Problems
Makoto Yamashita, Masaki Kimizuka, Sunyoung Kim
SIAM Conference on Optimization 2021 2021.7
Exactness Conditions for Semidefinite Relaxation of Nonconvex QCQPS with Forest Structures
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
SIAM Conference on Optimization 2021 2021.7
進化計算に対する親個体の分布を用いたステップサイズ適応の提案
武田龍之介, 山下真
第19回進化計算学会研究会 2021.3
非線形最適化問題に対する非実行可能 arc-search 内点法の数値実験による評価
飯田 英之介, Yaguang Yang, 山下真
最適化：モデリングとアルゴリズム 2019.3
手術スケジュール割り当てに関するモデルの提案およびその数値計算
黒田 航太朗, 山下真, 乾 文良, 志賀 卓弥, Malik Olivier Boussejra, George Radescu
2018年度日本経営工学会関東支部学生論文発表会 2019.3
A Cone Decomposition Method with Sparse Matrix for Mixed-Integer SOCP problem Invited International conference
Sena Safarina, Tim J. Mullin, Makoto Yamashita
ICCOPT 2019, the Sixth International Conference on Continuous Optimization 2019.8
An Efficient Approach for Pooling Problems by Second-order Cone Programming Relaxations and Rescheduling Methods Invited International conference
Makoto Yamashita, Masaki Kimizuka, Sunyoung Kim
International Workshop on Control and Optimization 2018.11
対数行列式と l1 ノルム関数をもつ半正定値計画問題に対する非単調スペクトル射影勾配法
福田光浩, 中垣敬, 山下真
高度情報化社会に向けた数理最適化の新潮流 2018.8
AcceleratedModulus-BasedGauss-Seidel法の剛体シミュレーションへの応用
宮本 柊吾, 山下真
2018年度日本経営工学会関東支部学生論文発表会 2019.3
アニーリング手法の適用による道路修繕順序決め問題への数値解法
坂本優真, 山下真
2018年度日本経営工学会関東支部学生論文発表会 2019.3
Cone Decomposition Method for Mixed-Integer SOCP arising from tree breeding International conference
Sena Safarina, Makoto Yamashita
International Symposium on Mathematical Programming 2018.7
A polyhedral based method for optimal contribution selection problem
Sena Safarina, Makoto Yamashita, Tim J. Mullin
高度情報化社会に向けた数理最適化の新潮流 2018.8
A path-following method for semidefinite programming without Slater condition International conference
Makoto Yamashita, Kei Takemura
International Symposium on Mathematical Programming 2018 2018.7
強度変調放射線治療におけるビーム強度計算への逐次線形計画最適化手法の構築
岸本祥吾, 山下真
日本オペレーションズ・リサーチ学会 ヘルスケアのOR研究部会 第３回 2019.11
交通最適化問題に対するQRAO適用に関する検討
素川慎司, 山下真
日本オペレーションズ・リサーチ学会2024春季研究発表会 2024.3
An infeasible interior-point arc-search method with Nesterov's restarting strategy for LP
飯田英之介, 山下真
日本オペレーションズ・リサーチ学会2024春季研究発表会 2024.3
共役勾配パラメータを凸結合で組み合わせた共役勾配法のリーマン多様体上への拡張
三浦崚太郎, 山下真
日本経営工学会関東支部2023年度学生論文発表会 2024.2
Generalized Transfer Learning Using Sparsity and Hyperparameter Selection via Nonsmooth Bilevel Optimization
伊藤 拓巳, 山下真
日本応用数理学会第20回研究部会連合発表会 2024.3
ジョブショップスケジューリング問題に対する量子緩和解法における量子ビットの圧縮率と数値実験
川澄朋章, 山下真
日本経営工学会関東支部2023年度学生論文発表会 2024.2
制約付き多項式最適化問題に対するthird-order tensor空間上の半正定値計画緩和 Invited
丸茂弘紀, 山下真
シンポジウム：錐線形計画とその周辺 2024.2
樹木園種別構成問題に現れる錐最適化問題への効率的な解法の構築 Invited
山下真, Tim J. Mullin, Sena Safarina
日本オペレーションズ・リサーチ学会 研究部会 最適化とその応用 2018.5
An efficient nonmonotone spectral projected gradient method for semidefinite program with log-determinant and l1-norm function International conference
Mituhiro Fukuda, Takashi Nakagaki, Makoto Yamashita
Nonlinear Analysis and Convex Analysis 2017 2017.7
Differential Evolution for Solving Maximum Clique Problem International conference
Fang Hui, Makoto Yamashita
SIAM Conference on Optimization 2017 2017.5
一般化優対角行列による緩和を用いた Pooling Problem に対する解法の構築
君塚柾貴, Sunyoung Kim, 山下真
日本オペレーションズ・リサーチ学会 2018年春季研究発表会 2018.3
最適構成問題に対するLPP 緩和に基づいた整数計画問題による定式化
Sena Safarina, Makoto Yamashita
数理最適化の発展：モデル化とアルゴリズム 2017.8
A Fast SOCP-based Method for Optimal Selection Problem in Tree Breeding International conference
Makoto Yamashita, Tim J Mullin, Sena Safarina
INFORMS Annual Meeting 2016 2016.11
Mixed-integer SOCP in optimal contribution selection of tree breeding International conference
Makoto Yamashita, Sena Safarina, Tim J Mullin
Workshop on Advances in Optimization 2016.8
A Steep-Ascent Method for MI-SOCP arising from Tree Breeding International conference
Makoto Yamashita, Tim J Mullin, Sena Safarina
SIAM Conference on Optimization 2017 2017.5
A Lifted-Polyhedral-Programming Approach for Optimal Contribution Problems International conference
Sena Safarina, Makoto Yamashita
SIAM Conference on Optimization 2017 2017.5
High-performance Implementation of Positive Matrix Completion for SDPs International conference
Makoto Yamashita, Kazuhide Nakata
INFORMS Annual Meeting 2013 2013.10
半正定値計画問題に対する行列補完理論の高速実装 Invited
山下 真
オペレーションズ・リサーチ学会「最適化の理論と応用」研究部会 2012年度第３回 2012.12
対数行列式半正定値計画問題に対する双対スペクトラル射影勾配法の構築
山下真, 福田光浩, 中垣敬
日本オペレーションズ・リサーチ学会 2014年春季研究発表会 2014.3
High Performance Solvers for Semidefinite Programs International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
KSIAM Annual Meeting 2011 2011.11
Parallel Computation for SDPs Focusing on the Sparsity of Schur Complements Matrices International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhide Nakata, Maho Nakata
INFORMS Annual Meeting 2011 2011.11
センサーネットワークモデルにおける重み付けによる数値精度向上について
金城 憲長, 山下 真, 福田 光浩, 下平 英寿
日本オペレーションズ・リサーチ学会 2012年秋季研究発表会 2012.9
An approach based on shortest path and connectivity consistency for sensor network localization problems International conference
Makoto Yamashita, I-Lin Wang
The International Symposium on Mathematical Programming 2012 2012.8
Efficient Parallel Software for Large-Scale Semidefinite Programs International conference
Makoto Yamashita, Katsuki Fujisawa
2010 IEEE Multi-Conference on Systems and Control 2010.9
Ellipsoid-type Confidential Bounds on Semi-algebraic Sets via SDP Relaxation International conference
Makoto Yamashita, Masakazu Kojima
Siam Conference on Optimization 2011 2011.5
SDPARA:a parallel software for large-scale SDP based on primal-dual interior-point methods
Makoto Yamashita
Parallel Computing and SDP Workshop 2010.12
A Successive LP Approach with C-VaR Type Constraints for IMRT Optimization International conference
Shogo Kishimoto, Makoto Yamashita
International Conference on Continuous Optimization 2016 2016.8
An Iterative Method using Boundary Distance for Box-constrained Nonlinear Semidefinite Programs International conference
Akihiro Komatsu, Makoto Yamashita
International Conference on Continuous Optimization 2016 2016.8
A Numerically Stable Primal-Dual Interior-Point Method for SDP International conference
Kei Takemura, Makoto Yamashita
International Conference on Continuous Optimization 2016 2016.8
直交射影作用素を用いた無線センサーネットワーク位置推定アルゴリズムの解析
城戸武尊, 山下真
日本オペレーションズ・リサーチ学会 2016年春季研究発表会 2016.3
Optimising selection in tree breeding with constraints on relatedness and operational flexibility International conference
Tim. J. Mullin, Makoto Yamashita, Pietor Belotti
Forest Genetics for Productivity Conference 2016.3
An Efficient Second-Order Cone Programming Approach for Optimal Selection in Tree Breeding International conference
Sena Safarina, Tim J Mullin, Makoto Yamashita
International Conference on Continuous Optimization 2016 2016.8
センサーネットワーク位置推定問題に対する二次錐計画問題を用いた精度の向上
曽根毅, 山下真
日本オペレーションズ・リサーチ学会 2016年春季研究発表会 2016.3
錐最適化問題による樹木園種別構成問題の定式化とその求解
山下真, Tim Mullin
「新時代の最適化モデルに基づく意思決定支援プラットフォームの研究と開発」シンポジウム 2014.9
Dual Approach Based on Spectral Projection Gradient Method for log-det SDP with ell_1 Norm International conference
Makoto Yamashita, Mituhiro Fukuda, Takashi Nakagaki
SIAM Conference on Optimization 2014 2014.5
SDPA family: High-performance solvers for semidefinite programming Invited International conference
Makoto Yamashita
Workshop on Systems Management and Control 2015.12
A Semi-definite Programming Approach for Optimal Selection in Tree Breeding International conference
Makoto Yamashita, Tim Mullin
INFORMS Annual Meeting 2014 2014.11
Computational prospects on copositive programming
Modeling and Optimization Theory 2006
Parallel Implementation for SemiDefinite Programming with Positive Definite Matrix Completion International conference
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata
International Conference on Continuous Optimization 2004.8
Parallel Implementation for SemiDefinite Programming withPositive Matrix Completion Method
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata
SAOR 2004.6
Prospects on copositive programming
19th International Symposium on Mathematical Programming 2006
SDPA (SemiDefinite Programming Algorithm) and its Parallel/Completion versions International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata
Informs Annual Meeting 2005 2005
High Performance Grid and Cluster Computing for Some Optimization Problems
Proceedings of SAINT 2004 Work Shops 2004
Parallel Computation for SemiDefinite Programming International conference
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima
The International Symposium on Mathematical Programming 2003 2003.8
Primal-Dual Interior-Point Methods of SemiDefinite Programs International conference
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima
CORS/Informs Joint Meeting 2004.5
Primal-Dual Interior-Point Methods of SemiDefinite Programs International conference
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima, Kazuhide Nakata
SIAM Conference on Parallel Processing for Scientific Computing 04 2004.2
PC クラスタ上における半正定値計画問題の並列計算
山下真, 藤沢克樹, 小島政和
SAOR 2003.6
SDPA: Leading-edge software for SDP International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
Informs Annual Meeting 2008 2008.10
Accurate electronic structure calculations using semidefinite programming software
INFORMS Optimization Society: Theory, Computation, and Emerging Applications 2008
Enclosing Ellipsoids of Semi-algebraic Sets and Error Bounds in Polynomial Optimization International conference
Makoto Yamashita, Masakazu Kojima
Nonlinear Optimization, Variational Inequalities and Equilibrium Problems 2010.7
Parallel Software for SemiDefinite Programming with Sparse Schur Complement Matrix International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Yoshiaki Futakata, Kazuhiro Kobayashi, Kazuhide Nakata, Maho Nakata
The International Symposium on Mathematical Programming 2009 2009.8
Computational time estimation of SDP solvers International conference
Makoto Yamashita, Kazuhide Nakata
Informs Annual Meeting 2007 2007.11
量子化学における超大規模半正定値計画問題と並列計算による高速求解
山下 真
第20回 RAMP シンポジウム 2006.10
Exploiting the semidefinite programming formulation of the variational calculation on second-order reduced density matrix of the atoms and molecules
Odyssey 2008: Mathematical and Computational Aspects of Molecular Electronic Structure Calculation 2008
Approximations of electronic structures of atoms and molecules by semidefinite programming
The 4th Sino-Japanese Optimization Meeting 2008
Large-scale semidefinite programming from quantum chemistry International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata, Maho Nakata
The International Symposium on Mathematical Programming 2006 2006.7
Parallel Interior-Point Methods for Large Semi-Definite Programming International conference
Makoto Yamashita, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuhide Nakata
SIAM Conference on Parallel Processing for Scientific Computing 2006 2006.2
半正定値計画問題に対する並列実装
山下真, 藤沢克樹, 小島政和
数値解析シンポジウム2003 2003.5
半正定値計画問題を解くソフトウェアのPCクラスタ上における並列実装
山下真, 藤沢克樹, 小島政和
日本オペレーションズ・リサーチ学会春季研究発表会 2003.3
Parallel implementation of SDPA (SemiDefinite Programming Algorithm) on PC cluster International conference
Makoto Yamashita, Katsuki Fujisawa, Masakazu Kojima
The Second Japanese-Sino Optimization Meeting 2002 2002
時間制約付き carrier vehicle routing 問題に対する二次錐計画問題を用いた発見的解法
脇田康平, 山下真
日本経営工学会関東支部2022年度学生論文発表会 2023.3
グリーン配送計画問題に対するNSGA-II を用いた発見的解法の構築
遠藤智弘, 山下真
日本経営工学会関東支部2022年度学生論文発表会 2023.3
構造的制約を持つ最適化問題に対する majorization-minimization 手法の構築
山川智也, 劉 田香, 山下真
日本オペレーションズ・リサーチ学会2023春季研究発表会 2023.3
Sample Average Approximation 法による確率制約条件付きの手術スケジュール最適化
竹村航, 陳暁薇, 山下真
日本オペレーションズ・リサーチ学会2023春季研究発表会 2023.3
Exactly Solving a class of QCQPs via Semidefinite Relaxation with Bipartite Sparsity Patterns
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
International Workshop on Continuous Optimization 2022.12
Conic Optimization for Drone Ship Routing Problem
Ning-Wen Yang, Makoto Yamashita
International Guest Lecture, World Class Professor 2022.11
Domain-space conversion と Block factor-width-2 decomposition による疎な半正定値計画問題の高速化
正木崚雅, 山下真
日本経営工学会関東支部2022年度学生論文発表会 2023.3
An Adaptation of Dual Spectral Projected Gradient Method
Namchaisiri Charles, Liu Tianxiang, Makoto Yamashita
International Workshop on Continuous Optimization 2022.12
対数行列式半正定値計画問題に対する双対射影勾配法の拡張
Namchaisiri Charles, Liu Tianxiang, 山下真
最適化：モデリングとアルゴリズム 2022.3
クラスタリング情報つき半正定値計画問題に対する双対解法
Namchaisiri Charles, 劉 田香, 山下真
日本オペレーションズ・リサーチ学会2022春季研究発表会 2022.3
A Modified Splitting Lagrangian Multiplier Method for Semi-Integer Problem
Sena Safarina, Makoto Yamashita
SIAM Conference on Optimization 2023 2023.6
Iterative Local Methods Based on Second-Order Cone Programming for Ship Routing Problem with Two Drones
Ning-wen Yang, Makoto Yamashita
SIAM Conference on Optimization 2023 2023.5
An Efficient Dual SPG Method for Log-Det SDP with Hidden Clustering Structure
Charles Namchaisiri, Liu Tianxiang, Makoto Yamashita
SIAM Conference on Optimization 2023 2023.6
Tight Semidefinite Relaxations for Sign-Indefinite Qcqps with Bipartite Structures
Godai Azuma, Mituhiro Fukuda, Sunyoung Kim, Makoto Yamashita
SIAM Conference on Optimization 2023 2023.6
強度変調放射線治療における不確実性を考慮した逸脱量最小化手法の開発
玉井正朗, 山下真
日本オペレーションズ・リサーチ学会 2021年春季研究発表会 2021.3
A Conic Relaxation Approach for Semi-Integer arising from Tree Breeding
Sena Safarina, Makoto Yamashita
2021.3
二次錐計画問題を用いた等式制約付き多項式最適化問題に対する緩和手法
岡田智之, Sunyoung Kim, 山下真
日本オペレーションズ・リサーチ学会 2020年春季研究発表会 2020.3
多面体の直径に対する推定上界についての数値評価
石川雄大, 山下真
2019年度日本経営工学会関東支部学生論文発表会 2020.2
確率制約条件付きの手術室割り当てに対する数値解法
黒田 航太朗, 山下真, 乾 文良, Olivier Boussejra Malik, 志賀 卓弥
日本オペレーションズ・リサーチ学会 2021年春季研究発表会 2021.3
三重対角性を持つ二次制約付き二次計画問題の狭小な半正定値計画緩和
東悟大, 福田光浩, 山下真, Sunyoung Kim
京都大学数理解析研究所 共同研究(グループ型) 数理最適化の理論・アルゴリズム・応用 2020.8
An efficient mathematical approach for optimal selection problems in tree breeding International conference
Makoto Yamashita, Sena Safarina, Tim J. Mullin, Satokoro Moriguchi
ISACIT 2019, 2019 International Symposium for Advanced Computing and Information Technology 2019.8
A dual spectral projected gradient method for logdeterminant semidefinite problems International conference
Makoto Yamashita, Mituhiro Fukuda, Sunyoung Kim, Takashi Nakagaki
ICCOPT 2019, the Sixth International Conference on Continuous Optimization 2019.8
High-rank Solution of Sum-of-Squares Relaxations for Exact Matrix Completion Invited International coauthorship International conference
Godai Azuma, Sunyoung Kim, Makoto Yamashita
The 25th International Symposium on Mathematical Programming 2024.7
Dual Spectral Projected Gradient Method for Generalized Log-det Semidefinite Programming International conference
Charles Namchaisiri, Makoto Yamashita
The 25th International Symposium on Mathematical Programming 2024.7
Conic Optimization Approaches to Cooperative Routing Problem and Polynomial Optimization Invited International coauthorship International conference
Makoto Yamashita
The 20th Annual Meeting & International Conference of the OR Society of TAIWAN 2024.11
Wasserstein 重心に対する内点安定化
栫光之助, 山下真
日本経営工学会関東支部2024年度学生論文発表会 2025.2
予算制限付き組合せバンディット問題におけるトンプソンサンプリングを用いた提案
南原涼也, 山下真
日本経営工学会関東支部2024年度学生論文発表会 2025.2
当院ドクターカーにおける多職種診療の最適化に関する研究
岩崎陽平, 小林和博, 山下真, 中田和秀, 森周介, 山田知世, 北原嶺, 原島瑞葵, 服部恭平, 森下 幸治
第52回日本集中治療医学会学術集会 2025.3
移動時間に対するペナルティを導入したドローン付き配送計画問題の近傍探索解法
三枝健也, 山下真
日本経営工学会関東支部2024年度学生論文発表会 2025.2
Exact Semidefinite Relaxations for Safety Verification of Neural Network Invited International coauthorship International conference
Godai Azuma, Sunyoung Kim, Makoto Yamashita
2025 International Conference on Continuous Optimization 2025.7
Semidefinite Programming Relaxation Hierarchy Using Third-Order Tensors for Constrained Polynomial Optimization International coauthorship International conference
Makoto Yamashita, Hiroki Marumo, Sunyoung Kim
2025 International Conference on Continuous Optimization 2025.7
A Collection of Discontinous Function for Global Optimization Benchmarking
Peicong Cheng, Makoto Yamashita
日本オペレーションズ・リサーチ学会2025秋季研究発表会 2025.9
超直方体入力下のニューラルネット安全性検証における狭小な半正定値計画緩和 International coauthorship
東悟大, 山下真, Sunyoung Kim
日本オペレーションズ・リサーチ学会2025秋季研究発表会 2025.9
当院ドクターカー病院前救急医療体制における出動要請基準に関する検討 International coauthorship International conference
岩﨑陽平, 知念優, 山下真, 北原嶺, 原島瑞葵, 服部恭平, 森周介, 小林和博, 中田和秀, 森下幸治
第53回日本救急医学会総会・学術集会 2025.10
遺伝的アルゴリズムに基づく Carrier Vehicle Traveling Salesman Problem の探索手法 International coauthorship International conference
小井戸大河, 山下真
日本経営工学会関東支部2025年度学生論文発表会 2026.3
2hop-2 次最短経路問題に対する状態空間の拡張を用いたアルゴリズム International coauthorship International conference
鈴木陽太, 山下真
日本経営工学会関東支部2025年度学生論文発表会 2026.3
研究交流賞
2019.10 日本経営工学会関東支部
Outstanding research achievement and contribution
2019.8 Asia Pacific Society for Computing and Information Technology
YAMASHITA Makoto
研究賞奨励賞
2013.9 日本オペレーションズ・リサーチ学会
山下 真
挑戦的研究賞
2013.8 東京工業大学
山下 真
手島精一記念研究賞博士論文賞
2005 手島工業教育資金団
山下 真
船井情報科学振興賞
2003 船井情報科学振興財団
小島政和, 進藤晋, 中田和秀, 原辰次, 藤沢克樹, 水野眞治, 山下真, 吉瀬章子
Numerical methods for cooperative routing problems based on conic optimization International coauthorship
Grant number：24K14836 2024.4 - 2028.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4680000 （ Direct Cost: \3600000 、 Indirect Cost：\1080000 ）
An improved dual projected gradient method for log-determinant semidefinite problems International coauthorship
Grant number：21K11767 2021.4 - 2024.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Authorship：Principal investigator Grant type：Competitive
Grant amount：\3900000 （ Direct Cost: \3000000 、 Indirect Cost：\900000 ）
Theory and algorithms for ill-conditioned conic linear programming
Grant number：20H04145 2020.4 - 2024.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
Muramatsu Masakazu
Grant amount：\17030000 （ Direct Cost: \13100000 、 Indirect Cost：\3930000 ）
A small-gain theorem leveraging the characteristics of the Rectified Linear Unit, commonly used in machine learning, was derived. Next, the semidefinite programming (SDP) relaxation conditions for quadratic constrained quadratic programming (QCQP) were analyzed, demonstrating applicability to forest structures and simultaneously tridiagonalizable cases. Additionally, an algorithm guaranteeing convergence to points satisfying strong optimality conditions (SOSP points) under ill-conditioned SDP was developed, enhancing local convergence compared to traditional methods. Other research also included stability analysis of recurrent neural networks, improvements in constrained optimization problems on the positive semidefinite cone, and QCQP analysis using bipartite graphs. Furthermore, a theory for the complete solving ill-conditioned SDPs was established.
Efficient optimization method for optimal contribution problems with semi-integer constraints
Grant number：18K11176 2018.4 - 2021.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Yamashita Makoto
Authorship：Principal investigator Grant type：Competitive
We developed efficient numerical methods for optimization contribution problems with semi-integer variables. The cone decomposition method allows to obtain cutting planes in an analytical form, and this leads to a numerical method that iteratively solves mixed-integer linear programming with semi-integer variables. We modified a splitting approach that splits the main problem into sub problems for semi-integer constraints and cone constraints. By including certain constraints, we improved the solution quality.
An Efficient Numerical Method for Optimal Contribution Problem based on Conic Optimization
Grant number：15K00032 2015.4 - 2019.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Yamashita Makoto, FUKUDA mituhiro, KOJIMA masakazu, NAKATA kazuhide, KIM sunyoung, MULLIN tim j., SAFARINA sena
Authorship：Principal investigator Grant type：Competitive
Optimal contribution problems arising from tree breeding or other optimization problems can be formulated as a mixed-integer second-order cone programming problem. We propose fast numerical methods that exploits conic optimization approaches. The proposed linear approximation reduces the computation time to about 1/10 of an existing method for obtaining exact solutions. Another new method, a steep ascent method, cannot theoretically guarantee the optimality, but it successfully outputs a favorable solution in several seconds.
Accelerated (sub)gradient methods for large-scale convex optimization problems - with emphasis in the theoretical aspects of the implementation and its applications -
Grant number：26330024 2014.4 - 2018.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Fukuda Mituhiro, YAMASHITA Makoto, ITO Masaru
Grant amount：\2860000 （ Direct Cost: \2200000 、 Indirect Cost：\660000 ）
In the current information society where large amount of data can be easily obtained and stored, there is a urgent need to solve large-scale convex optimization problems that can retrieve only valuable information (from that data). Very recently, the so-called accelerated (sub)gradient methods have been focused because they are easy to implement, but are very hard to understand theoretically. In this project, we analyze some properties that well-known (sub)gradient methods should satisfy in order to find some essential properties which guarantee fast convergence of these methods. And then, based on these properties, we propose a new family of (sub)gradient methods.
As a secondary theme, we proposed customized methods which work only with the function and gradient values for convex optimization problems which have special structures. We also conducted some numerical experiments to confirm their performance.
An iterative method for nonlinear semidefinite programming with the distance information to a cone boundary
Grant number：24710161 2012.4 - 2015.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)
YAMASHITA Makoto
Authorship：Principal investigator Grant type：Competitive
Nonlinear semidefinite programs are optimization problems with a constraint on the eigenvalues of a variable matrix, and the range of applications includes optimization with uncertainty and financial engineering.
We propose an iterative method for box-constrained nonlinear semidefinite programs using the distance information from the current point to the boundary of a positive semidefinite cone.
We verified through numerical tests that the proposed method is more effective for box-constrained problems that have strongly nonlinear functions than a feasible direction method.
A new paradigm in conic optimization: Optimization over the doubly nonnegative cone and software development
Grant number：23310099 2011.4 - 2015.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
YOSHISE Akiko, YAMAMOTO Yoshitsugu, KUNO Takahito, SHIGENO Maiko, HACHIMORI Masahiro, FUJISAWA Katsuki, YAMASHITA Makoto, WAKI Hayato
Grant amount：\11050000 （ Direct Cost: \8500000 、 Indirect Cost：\2550000 ）
The aim of this study is to propose new algorithms for solving a conic optimization problem, the doubly nonnegative optimization problem which is an optimization problem over the doubly nonnegative cone. Conic optimization includes a wide range of convex optimization problems, e.g., linear programs and semidefinite programs. There have been many studies that provide evidence of effectiveness of the semidefinite relaxation for combinatorial optimization problems and several commercial software packages for solving semidefinite programs have been developed. Our recent experiments showed that a tighter relaxation, the doubly nonnegative relaxation, is quite efficient for some classes of combinatorial optimization problems. However, in spite of its efficiency, it sometimes takes a quite long time to solve the doubly nonnegative programs using existing algorithms. To overcome the difficulty, we proposed an algorithm based on a new idea, implemented and improved it.
Numerical methods for large sensor network localization problems
Grant number：22310089 2010 - 2012
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
KOJIMA Masakazu, OKAMOTO Yoshio, MIYOSHI Naoto, YAMASHITA Makoto, FUJISAWA Katsuki
Grant amount：\14950000 （ Direct Cost: \11500000 、 Indirect Cost：\3450000 ）
Sensor network localization (SNL) problems have attracted considerable research interests for a broad spectrum of applications such as environmental monitoring, traffic control and structural assessment. The problem is to estimate the locations of n sensors of unknown positions using given distances and some m sensors of known positions (called anchors) in a sensor network of m+n sensors. Finding the solutions of this problem is known to be NP-hard. Thus, approximating the solution of this problem has been dealt with from many angles. In this project, we have studied numerical methods based on the semidefinite programming (SDP) relaxation．The SDP relaxation can provide approximate solutions with accuracy, but the computational cost of solving SNL problems by the SDP relaxation becomes expensive rapidly as their sizes increase. To avoid this difficulty, we fully exploited the sparsity which were involved in large scale SNL problems and improved the performance of the SDP solver SDPA. As a final product, we released a software package SFSDP that can solve large-scale sensor network localization problems in high speed.
疎行列に帰着される超大規模半正定値行列への並列計算による高速求解の実装
2009.4 - 2012.3
日本学術振興会 科学研究費若手研究（B）
山下 真
Authorship：Principal investigator Grant type：Competitive
A challenge to huge scale semidefinite programs-exploiting sparsity, parallel computation and polynomial optimization problems
Grant number：19310096 2007 - 2009
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
KOJIMA Masakazu, FUJISAWA Katsuki, TAKEDA Akiko, NAKATA Kazuhide, YAMASHITA Magkoto, FUKUDA Mituhiro, KIM Sunyoung
Grant amount：\19760000 （ Direct Cost: \15200000 、 Indirect Cost：\4560000 ）
We studied primal-dual interior-point methods for solving a semidefinite program which is one of the most important optimization problems having lots of applications in various fields of science and engineering, and developed a software package SDPA based on them. SDPA solves larger scale problems in shorter time than the existing software packages. As applications of SDPA, we provided SparsePOP for polynomial optimization problems and SFSDP for large scale sensor network localization problems.
超大規模な半正定値計画問題に対する効率的な並列計算の実装
2006 - 2009
日本学術振興会 科学研究費若手研究（B）
山下 真
Authorship：Principal investigator Grant type：Competitive
半正定値計画問題は、線形計画問題の対称行列空間への拡張であるが、制御理論から量子化学などさまざまな領域に応用をもっている。
しかしながら、実用的なサイズの応用を半正定値計画問題に定式化すると非常に大規模になってしまうことがある。
本研究では、この大規模な半正定値計画問題を並列計算を用いて効率的に解くことで、さまざまな応用に貢献することを目指す。
Effective Parallel Implementation for Extremely Large SemiDefinite Programming
2006 - 2009
Grant-in-Aid for Scientific Research
Grant type：Competitive
SemiDefinite Programming (SDP) is an extention of Linear Programming from vector spaces to symmetric matrix spaces.
It covers various fiedls such as control theory and quantum chemistry.
However, when we formulate prcatical applications into SDP, the size of SDP often becomes extremely large.
In this research, we apply parallel computation to solve extremely large SDPs efficently in short time.
多項式計画問題に対する大域的最適解法とその並列計算
Grant number：16016234 2004 - 2005
日本学術振興会 科学研究費助成事業 特定領域研究
小島 政和, 藤澤 克樹, 武田 朗子, 中田 和秀, 山下 真
Grant amount：\13000000 （ Direct Cost: \13000000 ）
本研究の主目的は凸最適化で蓄積された計算手法をさらに発展させ,クラスタおよびグリッド計算技術を融合し,非凸計画問題の中核をなす多項式計画問題および多変数多項式方程式系を計算効率良く解く並列計算手法・ソフトウェアを開発することにあった.以下の研究成果をあげた.
1.半正定値計画問題に対する主双対内点法ソフトウェアSDPAおよびその並列版の改良:これまで開発した単一CPUソフトウェアSDPA,並列版ソフトウェアSDPARA, SDPARA-Cがより一般的な形式の半正定値計画問題(具体的には,自由変数を含む問題)を扱えるように改良を行った.また,数値的な安定性を高め,精度を高めるための技術として,4倍精度計算を部分的に取り込むことに関して研究を行い,計算実験を通してその有効性を検証した.
2.凸緩和手法の開発・改良:平成16年度の研究により開発した多項式計画問題に対する疎性を活用した半正定値計画緩和計算機への実装を行い,計算実験を通してその有効性を検証した.また,多項式計画問題に等式条件が含まれる場合について,生成される緩和半正定値計画問題の数値的な不安定を解消するための研究を行った.さらに,疎性を活用した半正定値計画緩を対称錐上の多項式最適化問題へ拡張した.
3.多変数多項式方程式系のすべての複素孤立解を計算する多面体的ホモトピー法ソフトウェアPHoMの改良,並列版の開発:PHoMの並列版を開発し,これまで解くことの出来なかった超大規模な多項式方程式系の求解計算に成功した.また,多面体的ホモトピーの構築に必要な多項式方程式系の混合体積の新しい計算手法を提案し,その有効性を計算実験を通して検証した.
4.半正定値計画問題を解くためのソフトウェアであるSDPA, SDPARA-C, SDPARAに関するOnline Solverを構築し,その試験的運用を開始した.並列計算をも提供するOnline Solverは世界的にも例がない.
数理計画法
Institution：神奈川大学
計算数理基礎ー最適化
Institution：東京工業大学
数値解析学
Institution：東京工業大学
管理工学用数学第２
Institution：慶應義塾大学
数理最適化
Institution：東京工業大学
情報科学科総合演習・実験
Institution：東京工業大学
情報理論
Institution：東京工業大学
理学セミナー
Institution：東京工業大学
研究プロジェクト
Institution：東京工業大学
計算機支援数理
Institution：東京工業大学
経営工学基礎演習
Institution：神奈川大学
複雑系の解析
Institution：神奈川大学
ファイナンス工学
Institution：神奈川大学
工学基礎演習
Institution：神奈川大学
プログラミング演習第一
Institution：神奈川大学
