1998 Fiscal Year Final Research Report Summary
Numerical Methods for Large Scale Semidefinite Programming
| Project/Area Number |
09680418
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
社会システム工学
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KOJIMA Masakazu Tokyo Institute of Technology, Graduate School of Information Science and Engineering, Professor, 大学院・情報理工学研究科, 教授 (90092551)
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| Co-Investigator(Kenkyū-buntansha) |
SHIDA Masayuki Kanagawa University, Faculty of Engineering, Research Associate, 工学部, 助手 (20271364)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Semidefinite Programming / Mathematical Programming / Interior-Point Method / Combinatorial Optimization / Software / SDP Relaxation |
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| Research Abstract |
In this research project, we developed the SDPA (SemiDefinite Programming Algorithm) for solving large scale semidefinite programs. The main features of the SDPA are :
(a) The SDPA is written in C++.
(b) The SDPA incorporates the Mebrotra-type predictor-corrector step, which contributes to saving the number of iterations and to increasing the numerical stability.
(c) Besides the HRVW/KSH/M search direction the AHO search direction and the NT search direction are available at the user's option.
(d) The SDPA utilizes the Meschach to increase the numerical stability.
(e) The SDPA provides some information on infeasibility of a semidefinite program to be solved.
(f) The SDPA handles not only block diagonal matrices but also sparse matrix data structure. When an SDP to be solved is large scale and sparse, this sparse matrix data structure is effectively utilized in increasing the computational efficiency and saving the memory.
We applied the SDPA to various problems such as the semidefinite programming relaxation of nonconvex quadratic programming problems and bilinear matrix inequalities, and confirmed its computational efficiency through numerious computational experiments.
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