KOM 507E - Numerical Methods in Optimiz.

Course Objectives

To provide the definitions and the basic concepts related to optimization problem

To teach the unconstrained optimization methods ( line search and curve fitting methods).

To teach the constrained optimization methods(primal methods, penalty and barrier methods).

To gain experience about application of the optimization methods in optimal control.

Course Description

Definitions and basic concepts related to optimization problem (classification, algorithms, convergence, necessary and sufficient conditions for extremum, convexity etc.).Unconstrained optimization methods: line search methods (such as Fibonacci, golden section, Hooke and Jeeves, etc). Curve fitting methods (such as Davidon-Fletcher-Powell, Fletcher-Reeves, Newton, etc). Constrained Optimization methods: primal methods, penalty and barrier methods. Numerical application methods in optimal control theory (two-point boundary value problem and Riccati equation)