This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangean relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods.


Required Text

Bertsekas, Dimitri P. Nonlinear Programming. 2nd ed. Athena Scientific Press, 1999. ISBN: 1886529000.


Recommended Alternate Text

Bazaraa, Mokhtar S., Hanif D. Sherali, and C. M. Shetty. Nonlinear Programming: Theory and Algorithms. New York: John Wiley & Sons, 1993. ISBN: 0471557935.


Course Requirements

1. Weekly Problem Sets (about 12).
2. Midterm Examination (in-class, closed book).
3. Final Examination (3-hour exam).
4. Computer Exercises.

Grading

Grading will be based on the following: