Complexity analysis of interior-point algorithm based on a new kernel function for semidefinite optimization

Abstract

Interior-point methods (IPMs) for linear optimization (LO) and semidefinite optimization (SDO) have become a hot area in mathematical programming in the last decades. In this paper, a new kernel function with simple algebraic expression is proposed. Based on this kernel function, a primal-dual interior-point methods (IPMs) for semidefinite optimization (SDO) is designed. And the iteration complexity of the algorithm as O(n 3/4 log n/∈) with large-updates is established. The resulting bound is better than the classical kernel function, with its iteration complexity O(n log n/te) in large-updates case.