Instructor: Professor Katta G. Murty, 232 IOE Bldg., 763-3513, katta_murty@umich.edu

Prerequisites: A course in linear programming, equivalent to IOE 510.

Course objectives: To expose the student to nonlinear models, their applications, how to construct them, and to algorithms for solving them satisfactorily

Books:

1. M.S. Bazaraa, H.D. Sherali, and C.M. Shetty, Nonlinear Programming Theory and Algorithms, Wiley, 1993, 2nd Edition.
2. K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming, Helderman-Verlag, 1988.(This book is now available for download).
3. R. Fletcher, Practical Methods of Optimization, Wiley-Interscience, 1987.

Contents:

1. Formulation of continuous optimization models, curve fitting, parameter estimation, and -measures of deviation. Difference between linear and nonlinear model building. Examples.
2. Types of problems. State of the art. What can and cannot be done efficiently? Goals for algorithms.
3. Theorems of alternatives for linear systems.
4. Convex sets, separating hyperplanes, convex and concave functions.
5. Optimality conditions.
6. Quadratic programming and complementary pivot methods.
7. Newton's method and simplicial methods for nonlinear equations.
8. Line Search methods.
9. Unconstrained minimization algorithms.
10. Constrained minimization algorithms. Penalty and barrier methods, SQP and SLP methods.

Work in the course: Homeworks every week. One midterm and final. A computer project.

Lecture Notes (Transparencies):