Optimization Methods and Applications on problem solving with MATLAB in the presence of Randomness

Abstract

A review of iterative methods used to nd optimal solutions to large sparse linear systems including methods based on line search descent algorithms and Krylov subspace methods. We also detail how to use the MATLAB optimization toolbox to solve a variety of optimization problems including linear and non-linear problems in Chapter 2. A review of the classical Travelling Salesman Problem (TSP) is provided in Chapter 3 with examples of solved problems. In Chapter 4 we used a MATLAB program to investigate the effect that randomness has on a system of ODE's namely the equation of a harmonic pendulum, we demonstrate these effects with a number of plots in the phase-plane and with respect to the time t.