ECE 490

• Control Systems

Same as CSE 541

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.

• 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

The course objective is to provide seniors in Electrical or Computer Engineering with a basic understanding 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

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.

• Differential calculus
• Linear algebra
• Computer programming
• Ability to reason in abstract terms

D. P. Bertsekas, Nonlinear Programming, 1999, Athena Scientific, Belmont, MA.

Engineering Science: 1.5 credits or 50%
Engineering Design: 1.5 credits or 50%

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.

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

1. Formulate finite-dimensional optimization problems (1)

2. Apply some sufficiency conditions to an optimization method to test whether a minimum or a maximum exists, and whether they are unique (1)

3. Tell the difference between a local optimum and a global optimum (1)

4. Use the first- and second-order conditions for unconstrained optima to calculate minima and maxima (1)

5. Use various computational algorithms for unconstrained optimization, including steepest descent, Newton's method, conjugate-direction methods, and direct search methods (1)

6. Analyze convergence of the algorithms in 5 above (1)

7. Use software for numerical computation of minima and maxima (1, 6)

8. Obtain analytic solutions to some optimization problems with equality constraints, using Lagrange multipliers (1)

9. Obtain analytic solutions to some optimization problems with inequality constraints, again using Lagrange multipliers (1)

10. Use various computational algorithms for constrained optimization, including penalty function methods, primal and dual methods, penalty and barrier methods, and convex programming (1)

11. Analyze convergence of the algorithms in 10 above (1)

12. Conduct sensitivity analysis using Lagrange multipliers (1)

13. Use software for numerical computation of minima and maxima under constraints (1, 6)

14. Tell whether a linear programming problem has a solution or not (1)

15. Know what duality is in linear programming (1)

16. Employ the Simplex method in computing optimal solutions and write software that implements the Simplex method (1)

17. Formulate some engineering design problems as linear programs, and obtain optimum designs using available software packages (1, 2, 6)

18. Use both linear and nonlinear programming as effective tools to solve engineering design problems (1, 2, 6)