MAT 351E - Computational Optimization

Course Objectives

1- To teach the modeling and graphical solution of the optimization problems.
2- To teach the necessary and sufficient conditions for the local and global minimization.
3- To teach the methods of solutions of the single and multivariable functions in the unconstrained problems.
4- To teach the quadratic programming, penalty and barrier methods for the constrained optimization problems.
5- To teach the Simplex method for the solution of linear constrained optimization problems.
6- To show computer applications with up-to-date programing languages for the optimization problems.

Course Description

Problem formulation in optimization and their graphical solutions. Unconstrained Optimization; conditions for local minima. Line Search Methods; Golden Section method, Newton’s method. Multi Variable Problems; steepest descent method and scaling, conjugate gradient methods: The Fletcher and Reeves Method, Modified Newton Method, Marquardt Modification, Quasi-Newton methods: Davidon Fletcher Powel (DFP) method, Broyden Fletcher Goldfarb Shanno (BFGS) method. Least squares method, Trust-region methods. Linear and Nonlinear Constrained Optimization Problems; Lagrange multipliers, Kuhn-Tucker conditions, Sensitivity analysis, Quadratic programming, Penalty and Barrier methods, Simplex method.