Solving symmetric indefinite systems in an interior-point method for second order cone programming

Abstract

Many optimization problems can be formulated as second order cone programming (SOCP) problems. Theoretical results show that applying interior-point method (IPM) to SOCP has global polynomial convergence. However, various stability issues arise in the implementation of IPM. The standard normal equation based implementation of IPM encounters stability problems in the computation of search direction. In this paper, an augmented system approach is proposed to overcome the stability problems. Numerical experiments show that the new approach can improve the stability.