ECE 490
Introduction to Optimization

Displaying course information from Spring 2014.

Section Type Times Days Location Instructor
P3 DIS 1100 - 1220 T R   106B8 Engineering Hall  Rayadurgam Srikant
P4 DIS 1100 - 1220 T R   106B8 Engineering Hall  Rayadurgam Srikant
Web Page http://courses.engr.illinois.edu/ece490/
Official Description Basic theory and methods for the solution of optimization problems; iterative techniques for unconstrained minimization; linear and nonlinear programming with engineering applications. Course Information: Same as CSE 441. 3 undergraduate hours. 4 graduate hours. Prerequisite: ECE 190 and MATH 415.
Subject Area Control Systems
Course Prerequisites Credit in ECE 190
Credit in MATH 415
Course Directors Tamer Başar
Detailed Description and Outline

The course objective is to provide seniors in Electrical or Computer Engineering with a basic under-standing of optimization problems, viz., their formulation, analytic and computational tools for their solutions, and applications in different areas.

Topics:

  • Introduction and review of fundamentals
  • Unconstrained optimization
  • Optimization subject to equality constraints
  • Nonlinear programming
  • Linear programming
  • Selected topics from dynamic programming, large-scale programming, and multicriteria optimization

Same as CSE 541

Computer Usage
The students are assigned homework problems and are asked to write MATLAB programs for numerical optimization algorithms and run them on a workstation. Some basic MATLAB files for optimization are provided.
Topical Prerequisities
  • Differential calculus
  • Linear algebra
  • Computer programming
  • Ability to reason in abstract terms
  • Texts
    H. T. Jongen, K. Meer & E. Triesch, Optimization Theory, Kluwer, 2004.
    ABET Category
    Engineering Science: 1.5 credits or 50%
    Engineering Design: 1.5 credits or 50%
    Course Goals

    This course is taught once a year every spring semester, and is elective for seniors in electrical and computer engineering programs. Its main objective is to provide these students with a basic understanding of optimization problems, viz., their formulation, analytic and computational tools for their solutions, and applications in different areas.

    Instructional Objectives

    By the end of the semester, the students should be able to do the following:

    1. Formulate finite-dimensional optimization problems (a)

    2. Apply some sufficiency conditions to an optimization method to test whether a minimum or a maximum exists, and whether they are unique (a)

    3. Tell the difference between a local optimum and a global optimum (a)

    4. Use the first- and second-order conditions for unconstrained optima to calculate minima and maxima (a)

    5. Use various computational algorithms for unconstrained optimization, including steepest descent, Newton's method, conjugate-direction methods, and direct search methods (a)

    6. Analyze convergence of the algorithms in 5 above (a)

    7. Use software for numerical computation of minima and maxima (a, k)

    8. Obtain analytic solutions to some relatively simple optimization problems with equality constraints, using Lagrange multipliers (a)

    9. Obtain analytic solutions to some relatively simple optimization problems with inequality constraints, again using Lagrange multipliers (a)

    10. Use various computational algorithms for constrained optimization, including penalty function methods, primal and dual methods, penalty and barrier methods, and convex programming (a)

    11. Analyze convergence of the algorithms in 10 above (a)

    12. Conduct sensitivity analysis using Lagrange multipliers (a)

    13. Use software for numerical computation of minima and maxima under constraints (a, k)

    14. Tell whether a linear programming problem has a solution or not (a)

    15. Know what duality is in linear programming (a)

    16. Employ the Simplex method in computing optimal solutions and write software that implements the Simplex Method (a)

    17. Formulate some engineering design problems as linear programs, and obtain optimum designs using available software packages (a, c, k)

    18. Use both linear and nonlinear programming as effective tools to solve engineering design problems (a, c, k)

    Last updated: 5/23/2013