IE 614 Nonlinear Programming Spring 2003

Textbook:

• Nonlinear Programming by D.P. Bertsekas, Athena Scientific Press, 1999.
• Nonlinear Programming Algorithms, A. Nemirovski.
  

1.    Generalities
2.    Unconstrained Optimization: Necessary and Sufficient Conditions for Local Minima, Role of Convexity
3.    Quadratic Unconstrained Problems, Existence of Optimal Solutions, Iterative Computational Methods
4.    Gradient Methods, Details and Convergence Issues
5.    Rate of Convergence Issues
6.    Newton's Method and Variants, Least Squares and Gauss-Newton Method
7.    Conjugate Direction Methods, Quasi-Newton Methods, Non-derivative Mehtods
8.    Constrained Optimization: Optimization over a Convex Set, Optimality Conditions
9.    Feasible Directions Method, Gradient Projection Method
10.    Equality Constrained Problems, Basic Lagrange Multiplier Theorem
11.    Equality Constrained Problems, Sufficient Conditions, Augmented Lagrangians, Sensitivity Issues
12.    Inequality Constrained Problems, Karush-Kuhn-Tucker Optimality Conditions, Fritz-John Conditions, Constraint Qualifications
13.    Convex Cost and Linear Constraints, Duality Theorem, LP and QP duality
14.    Conic Duality and Semidefinite Programming
15.    Barrier and Interior Point Methods

We will follow closely the textbook in the order of topics specified above. This is an introductory course in nonlinear programming. Basic knowledge of linear algebra and some background on optimization are assumed. 

  Grading Policy

Grading will be based on occasional homework (50%) and a midterm test (25%) and a final examination (25%), the dates of which will be announced.
All written submitted work in hws and exams are assumed to be strictly personal. Any behavior in violation of the University Policy on Cheating is strongly discouraged.