High-accuracy solution of large-scale semidefinite programs

摘要

We present a first-order approach for solving semidefinite programs. The goal of this approach is to compute a solution of the semidefinite program (SDP) up to a high accuracy in spite of using only partial second-order information. We propose a hybrid approach that uses an accelerated projection method to generate an approximate solution and then switches to the quasiminimal residual algorithm (QMR) algorithm applied to a symmetrized version of the Alizadeh-Haeberly-Overton (AHO) system to improve this approximation. Some numerical experiments based on a number of random test examples illustrate the potential of this approach.