Sdpsol: a Parser/solver for Semideenite Programs with Matrix Structure

A variety of analysis and design problems in control, communication and information theory, statistics, combinatorial optimization , computational geometry, circuit design, and other elds can be expressed as semideenite programming problems (SDPs) or determinant maximization problems (max-det problems). These problems often have matrix structure, i.e., some of the optimization variables are matrices. This matrix structure has two important practical ramiications: rst, it makes the job of translating the problem into a standard SDP or max-det format tedious, and, second, it opens the possibility of exploiting the structure to speed up the computation. In this paper we describe the design and implementation of sdpsol, a parser/solver for SDPs and max-det problems. sdpsol allows problems with matrix structure to be described in a simple, natural, and convenient way. Although the current implementation of sdpsol does not exploit matrix structure in the solution algorithm, the language and parser were designed with this goal in mind.