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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…
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,…
Inverse-Optimization-Based Uncertainty Set for Robust Linear Optimization
Ayaka Ueta, Mirai Tanaka, Ken Kobayashi +1
We consider solving linear optimization (LO) problems with uncertain objective coefficients. For such problems, we often employ robust optimization (RO) approaches by introducing a…