Publishing type：Research paper (scientific journal)  

DOI： 10.1007/s10957-025-02887-y

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Publishing type：Research paper (scientific journal)   Publisher：Institute of Electronics, Information and Communications Engineers (IEICE)  

DOI： 10.1587/transfun.2025eap1035

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Authorship：Lead author   Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1109/ACCESS.2024.3368631

Scopus

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Authorship：Lead author   Publishing type：Research paper (scientific journal)  

DOI： 10.1080/02331934.2022.2142471

Scopus

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Publishing type：Research paper (international conference proceedings)   Publisher：IEEE  

DOI： 10.1109/icassp49660.2025.10888469

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In this paper, we propose an optimization-based method for robust phase retrieval problem where the goal is to estimate an unknown signal from a quadratic measurement corrupted by outliers. To enhance the robustness of existing optimization models with the $\ell_1$ loss function, we propose a generalized model that can handle DC (Difference-of-Convex) loss functions beyond the $\ell_1$ loss. We view the cost function of the proposed model as a composition of a DC function with a smooth mapping, and develop a variable smoothing algorithm for minimizing such DC composite functions. At each step of our algorithm, we generate a smooth surrogate function by using the Moreau envelope of each (weakly) convex function in the DC function, and then perform the gradient descent update of the surrogate function. Unlike many existing algorithms for DC problems, the proposed algorithm does not require any inner loop. We also present a convergence analysis in terms of a DC composite critical point for the proposed algorithm. Our numerical experiment demonstrates that the proposed method with DC loss functions is more robust against outliers compared to existing methods with the $\ell_1$ loss.

arXiv

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Other Link： https://arxiv.org/pdf/2604.07686v2

In this paper, we introduce an overall convex model incorporating a nonconvex regularizer. The proposed model is designed by extending the least squares term in the constrained LiGME model [Yata Yamagishi Yamada 2022] to fairly general smooth convex functions for flexible utilization of non-quadratic data fidelity functions. Under an overall convexity condition for the proposed model, we present sufficient conditions for the existence of a minimizer of the proposed model and an inner-loop free algorithm with guaranteed convergence to a global minimizer of the proposed model. To demonstrate the effectiveness of the proposed model and algorithm, we conduct numerical experiments in scenarios of Poisson denoising problem and simultaneous declipping and denoising problem.

arXiv

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Other Link： https://arxiv.org/pdf/2509.03258v2

Authorship：Lead author,　Corresponding author   Language：English  

DOI： 10.48550/arXiv.2506.05974

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In this paper, we address a nonconvexly constrained nonsmooth optimization
problem involving the composition of a weakly convex function and a smooth
mapping. To find a stationary point of the target problem, we propose a
variable smoothing-type algorithm by combining the ideas of (i) translating the
constrained problem into a Euclidean optimization problem with a smooth
parametrization of the constraint set; (ii) exploiting a sequence of smoothed
surrogate functions, of the cost function, given with the Moreau envelope of a
weakly convex function. The proposed algorithm produces a vector sequence by
the gradient descent update of a smoothed surrogate function at each iteration.
In a case where the proximity operator of the weakly convex function is
available, the proposed algorithm does not require any iterative solver for
subproblems therein. By leveraging tools in the variational analysis, we show
the so-called {\em gradient consistency property}, which is a key ingredient
for smoothing-type algorithms, of the smoothed surrogate function used in this
paper. Based on the gradient consistency property, we also establish an
asymptotic convergence analysis for the proposed algorithm. Numerical
experiments demonstrate the efficacy of the proposed algorithm.

arXiv

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Other Link： http://arxiv.org/pdf/2412.04225v2

We present an adaptive parametrization strategy for optimization problems
over the Stiefel manifold by using generalized Cayley transforms to utilize
powerful Euclidean optimization algorithms efficiently. The generalized Cayley
transform can translate an open dense subset of the Stiefel manifold into a
vector space, and the open dense subset is determined according to a tunable
parameter called a center point. With the generalized Cayley transform, we
recently proposed the naive Cayley parametrization, which reformulates the
optimization problem over the Stiefel manifold as that over the vector space.
Although this reformulation enables us to transplant powerful Euclidean
optimization algorithms, their convergences may become slow by a poor choice of
center points. To avoid such a slow convergence, in this paper, we propose to
estimate adaptively 'good' center points so that the reformulated problem can
be solved faster. We also present a unified convergence analysis, regarding the
gradient, in cases where fairly standard Euclidean optimization algorithms are
employed in the proposed adaptive parametrization strategy. Numerical
experiments demonstrate that (i) the proposed strategy succeeds in escaping
from the slow convergence observed in the naive Cayley parametrization
strategy; (ii) the proposed strategy outperforms the standard strategy which
employs a retraction.

arXiv

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Other Link： http://arxiv.org/pdf/2305.17901v1

Event date： 2023.8

Presentation type：Oral presentation (invited, special)  

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Presentation type：Oral presentation (invited, special)  

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Language：Japanese   Presentation type：Oral presentation (invited, special)  

File： KumeRAOTA2025_Web3.pdf

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Language：English   Presentation type：Oral presentation (invited, special)  

File： Kume-YamadaEUROPT2025.pdf

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