Kernel function with BFGS quasi-newton methods for solving nonlinear semi-definite problems

Abstract

In this paper, we will improve the practical performance of an interior points algorithm for convex nonlinear semi-definite optimization, where to minimize a nonlinear convex objective function subject to nonlinear convex constraints. We will propose a new method for solving this kind of problem by using a straightforward kernel function and the iterative Newton directions combined with the Broyden-Fletcher-Goldfarb-Shanno (BFGS in short) quasi-Newton method. Further, a best polynomial complexity for solving nonlinear convex problems will be found until now.