A trust region method for solving semidefinite programs

Authors:
Aiqun Huang;Chengxian Xu
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, P.R. China 430074;Department of Mathematics of School of Science, Xi'an Jiaotong University, Xi'an, P.R. China 710049
Venue:
Computational Optimization and Applications
Year:
2013

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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.