User's Manual for SparseCoLO: Conversion Methods for Sparse Conic-form Linear Optimization Problems

K. Fujisawa(fujisawachuo.ac.jp)
S. Kim(skimewha.ac.kr)
M. Kojima(kojimais.titech.ac.jp)
Y. Okamoto(okamotois.titech.ac.jp)
M. Yamashita(Makoto.Yamashitais.titech.ac.jp)

Abstract: SparseCoLO is a Matlab package for implementing the four conversion methods, proposed by Kim, Kojima, Mevissen, and Yamashita, via positive semidefinite matrix completion for an optimization problem with matrix inequalities satisfying a sparse chordal graph structure. It is based on quite a general description of optimization problem including both primal and dual form of linear, semidefinite, second-order cone programs with equality/inequality constraints. Among the four conversion methods, two methods utilize the domain-space sparsity of a semidefinite matrix variable and the other two methods the range-space sparsity of a linear matrix inequality (LMI) constraint of the given problem. SparseCoLO can be used as a preprocessor to reduce the size of the given problem before applying semidefinite programming solvers. The website for this package is http://www.is.titech.ac.jp/~kojima/SparseCoLO where the package SparseCoLO and this manual can be downloaded.

Keywords: Semidefinite program, Sparsity exploitation, Positive semidefinite matrix completion,

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Optimization Software and Modeling Systems

Citation: Research report B-453, Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, Tokyo 152-8552 Japan.

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Entry Submitted: 02/16/2009
Entry Accepted: 02/16/2009
Entry Last Modified: 02/16/2009

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