Research On The Interior-point Methods For Semidefinite Programming

Semidefinite programming (SDP) is an extension of linear programming (LO). In recent years, the theory and algorithms for SDP have developed greatly, and its most important applications are found in many fields. Interior-point methods (IPMs) for SDP have been studied intersively, due to their polynomial complexity and practical efficiency. IPMs have become the most important method to solve small or medium scale SDP problems.In this paper, we firstly introduce the theory, algorithm and recent research of semidefinite programming, then, introduce our work in IPMs for SDP. We conclude them as follows:1. we present a primal-dual interior-point algorithm for SDP based on an improved kernel function and derive the complexity analysis. We obtained the iteration bounds for large- and small-update methods..2. we present a new primal-dual infeasible interior-point algorithm for SDP with full-Newton steps by using a different fesasible steps and derive the complexity analysis.