Abstract

In this paper, we present a nonlinear programming algorithm for solving semidefinite programs (SDPs) in standard form. The algorithm's distinguishing feature is a change of variables that replaces the symmetric, positive semidefinite variable X of the SDP with a rectangular variable R according to the factorization X = RR T . The rank of the factorization, i.e., the number of columns of R, is chosen minimally so as to enhance computational speed while maintaining equivalence with the SDP. Fundamental results concerning the convergence of the algorithm are derived, and encouraging computational results on some large-scale test problems are also presented. Keywords: semidefinite programming, low-rank factorization, nonlinear programming, augmented Lagrangian, limited memory BFGS. 1 Introduction In the past few years, the topic of semidefinite programming, or SDP, has received considerable attention in the optimization community, where interest in SDP has included the investigation of...