Global Optimization Methods by Generalized Eigenvalue Computation

2016 Fiscal Year Final Research Report

• Project/Area Number: 26540007
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: The University of Tokyo
• Principal Investigator: Iwata Satoru 東京大学, 大学院情報理工学系研究科, 教授 (00263161)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 数理最適化 / 大域最適化 / 一般化固有値計算 / 機械学習 / 楕円体 / 信頼領域法

Outline of Final Research Achievements

Nonconvex optimization is believed to refuse any efficient algorithms in general. This project has aimed at developing a method to design efficient algorithms for nonconvex optimization problems that arises with a geometric background, exploiting their structures. In particular, we have designed an algorithm for computing the signed distance between overlapping ellipsoids. The running time is O(n^6), where n is the dimension of the space. We have extended this approach to solve the generalized CDT problem in the same running time. We have also reduced the trust-region subproblem, which is repeatedly solved in the trust-region method, to a generalized eigenvalue problem, and shown that this reduction leads to an efficient and accurate solution method with the aid of today's highly developed solvers for the generalized eigenvalue problem.

Free Research Field

数理工学