A new technique for global optimization methods

Abstract

We know that the necessary local optimality conditions are the main tools for the development of efficient numerical methods in local optimization. In this paper, we propose a new technique for global optimization methods. First we will introduce some new approach to obtain some verifiable global optimality conditions including some necessary global optimality conditions and some sufficient global optimality conditions. Then we will introduce how to use the obtained necessary global optimality conditions to design a new optimization method called strongly local optimization method and combining the new strongly local optimization method, some methods to improve the current strongly local minimizer and the obtained sufficient global optimality conditions to design some global optimization methods with some stopping criteria.