## IE 417: Nonlinear Programming

### Miscellaneous Handouts

### Lecture Slides

- Introduction
- Lecture 1: Mathematical Proof Techniques.
- Lecture 2: Introduction to Convex Analysis.
- Lecture 3: Convexity and Separation.
- Lecture 4: Convex Functions.
- Lecture 5: Maxima and Minima of Convex Functions.
- Lecture 6: Optimality Conditions (Unconstrained).
- Lecture 7: Optimality Conditions (Inequality Constrained).
- Lecture 8: Optimality Conditions (Equality Constrained).
- Lecture 9: Lagrangian Duality.
- Lecture 10: Saddle Point Optimality and the Dual Function.
- Lecture 11: Formulating the Lagrangian Dual.
- Lecture 12: Solving the Lagrangian Dual.
- Lecture 13: Introduction to Iterative Algorithms.
- Lecture 14: Line Search Algorithms.
- Lecture 15: Numerical Analysis Review.
- Lecture 16: Steepest Descent and Trust Region Methods.
- Lecture 17: Quasi-Newton Methods.
- Lecture 18: Conjugate Gradient Methods.
- Lecture 19: Penalty Methods.
- Lecture 20: Augmented Lagrangian Methods.
- Lecture 21: Barrier Methods.
- Lecture 22: Methods of Feasible Direction.
- Lecture 23: Reduced Gradient Methods.
- Lecture 24: Linear Complementarity Problem.
- Final Review.

### Assignments

- Problem Set #1 (due Sept 10)
- Problem Set #2 (due Sept 24)
- Problem Set #3 (due Oct 15)
- Problem Set #4 (due Nov 5)
- Problem Set #5 (due Nov 22)
- Problem Set #6 (due Dec 5)

### Reference Texts

- Nonlinear Programming: Theory and Algorithms, M.S. Bazaraa, H.D. Sherali, and C.M. Shetty.
- How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, Daniel Solow, Wiley (2001).
- How to Prove It: A Structured Approach, Daniel Velleman, Cambridge University Press (1994).

### Guides and Pointers on the Web

- Math World — an amazing on-line mathematics encyclopedia.
- The INFORMS OR/MS Resource Collection — an extensive collection of OR links
- NEOS Guide — a good overview of optimization
- e-Optimization.com
- Harvey Greenburg’s Courseware Page
- Harvey Greenburg’s Mathematical Programming Glossary
- John Mitchell’s Optimization Pointers

### On-line Tutorials, Case Studies, and Interactive Optimization

- IFORS tutORial Project
- NEOS Server — solve optimization problems over the Web
- Math Programming in Action
- Demonstration of Lagrangian Relaxation for the Traveling Salesman Problem.

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