2 citations · 3 across the 8 of their papers we have counts for
9 papers
An Improved Lower Bound for the Three-Dimensional Blaschke--Lebesgue Problem from Spectral and Dual Perspectives
Akatsuki Nishioka
The Blaschke--Lebesgue problem asks for convex bodies of minimum volume among all convex bodies of prescribed constant width. In the plane, the minimizer is the Reuleaux triangle,…
Revisiting Invex Functions: Explicit Kernel Constructions and Characterizations
Akatsuki Nishioka
An invex function generalizes a convex function in the sense that every stationary point is a global minimizer. Recently, invex functions and their subclasses have attracted attent…
A class of nonconvex semidefinite programming in which every KKT point is globally optimal
Akatsuki Nishioka, Yoshihiro Kanno
We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush--Kuhn--Tucker (KKT) conditions is globally optimal despit…
Pseudo-concave optimization of the first eigenvalue of elliptic operators with application to topology optimization by homogenization
Akatsuki Nishioka
We study optimization problems for the first eigenvalue of a linear elliptic operator. As applications, we consider homogenized two-phase optimal design problems, also known as top…
Variational analysis of unbounded and discontinuous generalized eigenvalue functions with application to topology optimization
Akatsuki Nishioka, Yoshihiro Kanno
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions…
A unified Euler--Lagrange system for analyzing continuous-time accelerated gradient methods
Mitsuru Toyoda, Akatsuki Nishioka, Mirai Tanaka
This paper presents an Euler--Lagrange system for a continuous-time model of the accelerated gradient methods in smooth convex optimization and proposes an associated Lyapunov-func…
A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization
Akatsuki Nishioka, Yoshihiro Kanno
Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's ext…
Convergence Rate Analysis of Continuous- and Discrete-Time Smoothing Gradient Algorithms
Mitsuru Toyoda, Akatsuki Nishioka, Mirai Tanaka
This paper addresses the gradient flow -- the continuous-time representation of the gradient method -- with the smooth approximation of a non-differentiable objective function and…
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,…