A robust algorithm for global optimization problems

Abstract

In this paper, a global optimization algorithm namely Kerk and Rohanin’s Trusted Region is used to find the global minimizers by employing an interval technique; with it, the algorithm can find the region where a minimizer is located and will not get trapped in a local one. It is able to find the convex part within the non-convex feasible region. This algorithm has descent property and global convergence. The numerical results have shown the algorithm has an outstanding capability in locating global minimizers.

Global Optimization Method For Minimizing Portfolio Selection Risk

“…For j = 0, y MTRM has proven to hold the descent property and global convergence. It has also shown its robustness capability of locating the global minimizers [7].…”

“…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].…”

“…This attribute allows MTRM to determine the convex parts within the given domain of a function. In other words, MTRM could separate a big non-convex problem into several small but convex ones [7].…”