Algorithm for Solution of Non-convex Optimization Problem Through Piece-wise Convex Transformation

Abstract

Optimization is central to any problem involving decision making. Thearea 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 Kerk and Rohanin’s Trusted Interval will be introduced. The method introduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only considers 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 globally convergent 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.

Global Optimization Method For Minimizing Portfolio Selection Risk

“…and the covariance of assets i and k could be represented by Equation (5). Then, the portfolio risk could be defined by Equation (6).…”

“…Hence, it is not comparable with HOPE. HSPM was improved further with better time complexity when the inner loop of its algorithm was altered slightly, giving rise to the algorithm called Improved Homotopy with 2-Step Predictor-corrector Method (I-HSPM) [6]. When extended, it resolves multi-variable optimization problems, and this gradient-based algorithm is now known as Modified Trusted Region Method (MTRM) [7].…”