Finding Sparse Solutions for Packing and Covering Semidefinite Programs

09/25/2018

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by   Khaled Elbassioni, et al.

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Packing and covering semidefinite programs (SDPs) appear in natural relaxations of many combinatorial optimization problems as well as a number of other applications. Recently, several techniques were proposed, that utilize the particular structure of this class of problems, to obtain more efficient algorithms than those offered by general SDP solvers. For certain applications, as those described in this paper, it is desirable to obtain sparse dual solutions, i.e., those with support size (almost) independent of the number of primal constraints. In this paper, we give such an algorithm, which is an extension of a logarithmic-potential based algorithm of Grigoriadis, Khachiyan, Porkolab and Villavicencio (SIAM Journal of Optimization 41 (2001)) for packing/covering linear programs.