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23 papers · 1 filter
Univariate representations of solutions to generic polynomial complementarity problems
Vu Trung Hieu, Alfredo Noel Iusem, Paul Hugo Schmölling +1
By using the squared slack variables technique, we demonstrate that the solution set of a general polynomial complementarity problem is the image, under a specific projection, of t…
On a minimization problem of the maximum generalized eigenvalue: properties and algorithms
Akatsuki Nishioka, Mitsuru Toyoda, Mirai Tanaka +1
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,…
Approximate Bregman Proximal Gradient Algorithm for Relatively Smooth Nonconvex Optimization
Shota Takahashi, Akiko Takeda
In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approxi…
Universal heavy-ball method for nonconvex optimization under Hölder continuous Hessians
Naoki Marumo, Akiko Takeda
We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and Hölder continuous Hessians. The proposed algorithm is a heavy-ball me…
Parameter-free accelerated gradient descent for nonconvex minimization
Naoki Marumo, Akiko Takeda
We propose a new first-order method for minimizing nonconvex functions with a Lipschitz continuous gradient and Hessian. The proposed method is an accelerated gradient descent with…
Convergence rate of the (1+1)-evolution strategy on locally strongly convex functions with lipschitz continuous gradient
Daiki Morinaga, Kazuto Fukuchi, Jun Sakuma +1
Evolution strategy (ES) is one of the promising classes of algorithms for black-box continuous optimization. Despite its broad successes in applications, theoretical analysis on th…