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ECE 58000 - Optimization Methods for Systems And Control

Lecture Hours: 3 Credits: 3

Areas of Specialization(s):

Automatic Control

Professional Attributes
EE Elective

Normally Offered: Each Spring

Catalog Description:
Introduction to optimization theory and methods, with applications in systems and control. Nonlinear unconstrained optimization, linear programming, nonlinear constrained optimization, various algorithms and search methods for optimization, and their analysis. Examples from various engineering applications are given.

Required Text(s):
  1. An Introduction to Optimization, 4th Edition, E. K. P. Chong and S. H. Zak, John Wiley & Sons, Inc., 2013, ISBN No. 9781118279014.

Recommended Text(s): None.

Lecture Outline:

Lectures Topics
1-3 INTRODUCTION - Motivating examples (1) - Mathematical preliminaries (2)
4-13 UNCONSTRAINED OPTIMIZATION - First and second order conditions (2) - Algorithms for unconstrained optimization: one dimensional search methods; gradient methods; Newton methods; conjugate direction methods; quasi-Newton methods (8)
14-16 LEAST SQUARES ANALYSIS - Examples and basic properties (2) - Recursive least squares algorithm (1)
17-19 RANDOM SEARCH ALGORITHMS - Simulated annealing (1) - Genetic algorithms (2)
20-28 LINEAR PROGRAMMING - Examples and basic properties (4) - Simplex method (2) - Duality (3)
29-38 NONLINEAR CONSTRAINED OPTIMIZATION - Lagrange and second order conditions (5) - Karush-Kuhn-Tucker and second order conditions (4) - Algorithms for constrained optimization (1)
39-42 CONVEX OPTIMIZATION - Convexity (2) - Optimality conditions (2)