On efficient algorithms for nonconvex feasibility problem and its applications

2019 Fiscal Year Final Research Report

• Project/Area Number: 16K05280
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Akita Prefectural University
• Principal Investigator: Matsushita Shin-ya 秋田県立大学, システム科学技術学部, 准教授 (20435449)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Keywords: 制約可能性問題 / 非凸集合 / 射影法

Outline of Final Research Achievements

This research aims to develop efficient methods for solving nonconvex feasibility problems. To deal with the non-convex constraint sets, we have investigated modification of a variety of optimization methods, such as fixed-point approximation methods, the proximal gradient method, the projection methods, the Douglas-Rachford method. In particular, we have presented some relevant convergence rate results for fixed-point approximation method and the proximal point algorithm. Moreover, we have investigated theoretical and numerical properties of the proposed methods.

Free Research Field

数理工学、応用数学

Academic Significance and Societal Importance of the Research Achievements

非凸制約集合は，制御工学における安定性や画像復元技術など，様々な分野で現れる重要な概念である。近年，非線形解析学の分野で研究されていた射影法が非凸集合に関連する制約可能性問題に有効であることが明らかになっているが，その理論的な収束の保証や収束率については解明されていないのが課題となっていた。