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# Optimization Methods for Systems and Control

## ECE58000

3

### Learning Objective:

• Use various methods to compute minimum or maximum of nonlinear functions of many variables
• Solve linear programming problems
• Find minimum or maximum of nonlinear functions of many variables using population-based methods
• Apply various optimization methods learned in the course to real-life design problems

### Description:

This course provides an introduction to various methods of obtaining the extremum (minimum or maximum) of a non-dynamical system and the use of these methods in real-life applications. Computational methods for nonlinear optimization; unconstrained optimization. Constrained optimization; linear programming; simplex method for solving linear programs; Lagrange's conditions, the Karush-Kuhn-Tucker (KKT) conditions, Least squares, Convex optimization, Global optimization methods: Genetic algorithms and Particle swarm optimization (PSO) method.

### Prerequisites:

MA 511 or equivalent (first graduate course in linear algebra) Linear algebra, calculus of several variables. In particular: matrix manipulation, linear spaces, quadratic forms, tangent planes. Elements of multivariable calculus, in particular, differentiation of real-valued functions of n variables, gradients, and the chain rule.

30 / 70

### Homework:

Approximately 5 homework assignments

None.

### Exams:

Two midterm exams; one final exam.

### Textbooks:

An Introduction to Optimization by E. K. P. Chong and S. H. Zak (4th edition), published by Wiley & Sons, Inc., New York 2013. Full text available online to Purdue students through Purdue Libraries.

### Computer Requirements:

ProEd minimum computer requirements. Access to MATLAB or the Student Edition of MATLAB (registered students can access via Purdue GoRemote--http://goremote.ics.purdue.edu).

MATLAB

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