Nonlinear Programming

**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:**

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

**Contents:**

- Formulation of continuous optimization models, curve fitting, parameter estimation, and -measures of deviation. Difference between linear and nonlinear model building. Examples.
- Types of problems. State of the art. What can and cannot be done efficiently? Goals for algorithms.
- Theorems of alternatives for linear systems.
- Convex sets, separating hyperplanes, convex and concave functions.
- Optimality conditions.
- Quadratic programming and complementary pivot methods.
- Newton's method and simplicial methods for nonlinear equations.
- Line Search methods.
- Unconstrained minimization algorithms.
- 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):**