Minimizing using BBO and DFO methods

Abstract

In [1], Nour and Zeidan proposed a numerical algorithm to solve optimal control problems involving sweeping processes. In order to apply this algorithm to real life problems, two numerical methods need to be developed: A numerical method to solve nonlinear differential equations, and a numerical method to nd the minimum of an objective function (given only numerically) in fi nite dimensional spaces. The goal of this thesis is to develop two MATLAB codes for the numerical algorithm of [1]. To solve nonlinear differential equations we use Runge-Kutta method of fourth order, and for the minimization part, we use two different methods, namely Nelder-Mead and Model Based Descent methods. Our codes are then applied to several examples and their efficiencies are discussed.