# Optimization Methods for Systems and Control

## ECE58000

3

### Learning Objective:

To familiarize students with current trends in optimization methods while at the same time equipping them with the tools necessary for advanced engineering design problems.

### Description:

An introduction to techniques, theory, and application of methods to obtain the extremum (minimum or maximum) of a non-dynamic system and the use of these methods in various applications. Linear programming; simplex method for solving linear programming problems, duality theory. Nonlinear optimization; unconstrained optimization, computational methods, constrained optimization, optimality conditions. Convex optimization and integer programming. Sp2018 ECE5800 Syllabus

### Topics Covered:

Unconstrained optimization; gradient methods, Newton's methods, quasi-Newton methods, conjugate-directions methods. Constrained optimization; linear programming, simplex method for solving linear programs; Lagrange's conditions, the Karush-Kuhn-Tucker (KKT) conditions. Genetic algorithms, Particle swarm optimization (PSO) method.

### Prerequisites:

Linear algebra, calculus of several variables (MA 511). In particular: matrix manipulation, linear spaces, quadratic forms, tangent planes. Elements of multivariable calculus, in particular, differentiation of real-valued functions of n variables, tangent planes, gradients, the chain rule.
You can review your linear algebra at your leisure by viewing video lectures by Professor Gilbert Strang at http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm.

### Applied / Theory:

30 / 70

https://mycourses.purdue.edu/

### Web Content:

On Blackboard: syllabus, grades, lecture notes, homework assignments, solutions, chat room, and message board.

### Homework:

Five (bi-weekly) assignments worth 100 pts.

None.

### Exams:

Two one-hour exams (100 pts each) and one two-hour final exam (200 pts).

### Textbooks:

Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative--Required: "An Introduction to Optimization", Edwin K. P. Chong and Stanislaw. H. Zak, 4th ed. 2013, John Wiley & Sons. ISBN: 978-1-1182-7901-4. http://www.engr.colostate.edu/~echong/book4/

### 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).

view

view