Design and implementation of a parser/solver for SDPs with matrix structure

Abstract

A wide variety of analysis and design problems arising in control communication and information theory, statistics, computational geometry and many other fields can be expressed as semidefinite programming problems (SDPs) or determinant maximization problems (maxdet-problems). In engineering applications these problems usually have matrix structure, i.e., the optimization variables are matrices. Recent interior-point methods can exploit such structure to gain huge efficiency. In this paper, we describe the design and implementation of a parser/solver for SDPs and maxdet-problems with matrix structure. The parser/solver parses a problem specification close to its natural mathematical description, solves the compiled problem efficiently, and returns the results in a convenient form.