2004 Fiscal Year Final Research Report Summary
Studies on Convex Optimization and Related Problems
| Project/Area Number |
14350046
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
FUKUSHIMA Masao Kyoto University, Graduate School of Informatics, Professor, 情報学研究科, 教授 (30089114)
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| Co-Investigator(Kenkyū-buntansha) |
CHEN Xiaojun Hirosaki University, Faculty of Science and Technology, Professor, 理工学部, 教授 (70304251)
YAMAKAWA Eiki Kansai University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (20289333)
YAMASHITA Nobuo Kyoto University, Graduate School of Informatics, Assistant Professor, 情報学研究科, 助手 (30293898)
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| Project Period (FY) |
2002 – 2004
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| Keywords | convex optimization / mathematical programming / algorithm / complementarity problem / iterative method |
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| Research Abstract |
Convex optimization is a basic research area which has been studied for a long time. It is also a very hot research area in which various applications of practical importance have recently been discovered as novel efficient solution methods such as interior point algorithms have been developed. The aim of this research is to develop practically efficient methods based on solid theoretical ground for solving convex optimization problems and related problems involving in particular constrained convex programming problems, positive semi-definite programming problems, and monotone complementarity problems, thereby contributing to expand the area of applications in engineering. The methods developed in this project are listed as follows : (1)Sequential quadratically constrained quadratic programming method for constrained convex programming problems ; (2)Regularized Newton method for minimizing convex functions with possibly singular Hessians ; (3)Active set identification technique in the proximal point method for monotone complementarity problems ; (4)Iterative methods for mathematical programs with equilibrium constraints ; (5)Smoothing Newton method for second-order cone complementarity problems ; (6)Matrix splitting method for second-order cone complementarity problems. Moreover, we introduced a new equilibrium concept in a non-cooperative game and studied it through a second-order cone complementarity problem. We have also studied nonlinear semidefinite programming problems and mathematical programs with equilibrium constraints under uncertainty. These studies will lead to our next research subject of robust optimization.
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