# ECE 58000 - Optimization Methods for Systems And Control

## Course Details

Lecture Hours: 3 Credits: 3

• EE Elective

Each Spring

### Campus/Online:

On-campus and online

MATLAB

### 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: With Applications to Machine Learning , 5th Edition , E. K. P. Chong, Wu-Sheng Lu, and S. H. Zak , John Wiley & Sons, Inc. , 2023 , ISBN No. 1119877636

None.

### Learning Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:
1. an ability to formulate optimization problems and identify possible solutions to such problems. [1]
2. an ability to apply and analyze basic linear and nonlinear optimization algorithms. [1]
3. a background needed to understand more advanced optimization techniques. [7]
4. an ability to make formal and rigorous arguments in analyzing optimization problems and solution techniques. [3]

### 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)

Homework, exams.