Algorithm for solution of non-convex optimization problem through piece-wise convex transformation

Abstract

Optimization is central to any problem involving decision making. The area of optimization has received enormous attention for over 30 years and it is still popular in research field to this day. In this paper, a global optimization method called Improved Homotopy with 2-Step Predictor-corrector Method will be introduced. The method in- troduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only consid- ers the convex part where minimizers existed on a function is applied. This mechanism allows the method to filter out concave parts and some unrelated parts automatically. The identified convex parts are called trusted intervals. The descent property and the global convergence of the method was shown in this paper. 15 test problems have been used to show the ability of the algorithm proposed in locating global minimizer.