, Volume 55, Issue 1, pp 49-71
Date: 08 Nov 2012

A trust region method for solving semidefinite programs

Abstract

When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.

This work is supported by National Natural Science Foundation of China 10971162.
An erratum to this article can be found at http://dx.doi.org/10.1007/s10589-013-9554-7.