Methods and applications for nonlinear second-order cone and semidefinite programming problems

2017 Fiscal Year Final Research Report

• Project/Area Number: 26730012
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Kyoto University
• Principal Investigator: Fukuda Hidemi 京都大学, 情報学研究科, 助教 (40726361)
• Research Collaborator: FUKUSHIMA Masao ; YAMASHITA Nobuo ; LOURENCO Bruno F. ; HU Ming
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 非線形２次錐計画問題 / 非線形半正定値計画問題 / 錐計画問題 / ２乗スラック変数 / ペナルティ法

Outline of Final Research Achievements

In this project, we considered methods for conic optimization problems,in particular,nonlinear programming (NLP), nonlinear second-order cone programming (SOCP), and nonlinear semidefinite programming (SDP). We first focused in two methods: differentiable exact penalty functions, and squared slack variables techniques.For both methods, the theoretical analysis,implementations and numerical experiments were successfully done using NLP, SOCP and SDP. For the slack variables technique, we also obtained results for more general symmetric conic problems.We further proposed a method called exact augmented Lagrangian for SOCP and SDP, which has some similarities with the exact penalty method.Moreover, we proposed a new DC method for general conic optimization problems. All the methods proposed and analyzed so far replace difficult conic problems with easier problems, that are well-understood by the community. Related to these, we also studied some methods for multiobjective problems.

Free Research Field

連続最適化