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.