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

DOI： 10.1016/j.orl.2024.107181

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Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

We study properties and algorithms of a minimization problem of the maximum generalized eigenvalue of symmetric-matrix-valued affine functions, which is nonsmooth and quasiconvex, and has application to eigenfrequency optimization of truss structures. We derive an explicit formula of the Clarke subdifferential of the maximum generalized eigenvalue and prove the maximum generalized eigenvalue is a pseudoconvex function, which is a subclass of a quasiconvex function, under suitable assumptions. Then, we consider smoothing methods to solve the problem. We introduce a smooth approximation of the maximum generalized eigenvalue and prove the convergence rate of the smoothing projected gradient method to a global optimal solution in the considered problem. Also, some heuristic techniques to reduce the computational costs, acceleration and inexact smoothing, are proposed and evaluated by numerical experiments.

DOI： 10.1007/s10589-024-00621-4

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Other Link： https://link.springer.com/article/10.1007/s10589-024-00621-4/fulltext.html

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Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

We consider a worst-case robust topology optimization problem under load uncertainty, which can be formulated as a minimization problem of the maximum eigenvalue of a symmetric matrix. The objective function is nondifferentiable where the multiplicity of maximum eigenvalues occurs. Nondifferentiability often causes some numerical instabilities in an optimization algorithm such as oscillation of the generated sequence and convergence to a non-optimal point. We use a smoothing method to tackle these issues. The proposed method is guaranteed to converge to a point satisfying the first-order optimality condition. In addition, it is a simple first-order optimization method and thus has low computational cost per iteration even in a large-scale problem. In numerical experiments, we show that the proposed method suppresses oscillation and converges faster than other existing methods.

DOI： 10.1007/s00158-023-03543-7

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Other Link： https://link.springer.com/article/10.1007/s00158-023-03543-7/fulltext.html

Authorship：Lead author   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

Abstract

We present an inertial projected gradient method for solving large-scale topology optimization problems. We consider the compliance minimization problem, the heat conduction problem and the compliant mechanism problem of continua. We use the projected gradient method to efficiently treat the linear constraints of these problems. Also, inertial techniques are used to accelerate the convergence of the method. We consider an adaptive step size policy to further reduce the computational cost. The proposed method has a global convergence property. By numerical experiments, we show that the proposed method converges fast to a point satisfying the first-order optimality condition with high accuracy compared with the existing methods. The proposed method has a low computational cost per iteration, and is thus effective in a large-scale problem.

DOI： 10.1007/s13160-023-00563-0

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Other Link： https://link.springer.com/article/10.1007/s13160-023-00563-0/fulltext.html

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

DOI： 10.14495/jsiaml.13.33

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