非線形微分方程式の数値解法を利用した最大固有値最小化問題の簡単な解法

Abstract

We present a simple numerical method for minimizing the maximum eigenvalues of real-valued symmetric matrices, based on nonlinear differential equation solvers. First, we convert the minimiza-tion problem for the maximum eigenvalues, which is nondifferentiable, into a differentiable optimiza-tion problem by means of interior point methods. Second, making use of differential equation solvers, we present a simple method for solving the optimization problem. Our method does not require optimization techniques such as the Newton method. Lastly, we demonstrate the effectiveness of the algorithm through some simulation experiments.