After successful completion of the course, students are able to distinguish between different types of nonlinear programming problems, to solve them with the appropriate methods, and to interpret the results (mostly economically).
NONLINEAR PROGRAMMING 1. Introduction 2. Classes of nonlinear optimization problems 3. Optimization with one variable 4. Optimization without restrictions with several variables 5. Optimization under equality constraints: The method of Lagrange 6. Optimization under equality and inequality constraints: The method of Karush-Kuhn-Tucker 7. Saddle-point formulation and convex optimization 8. Quadratic Programming 9. Separable Programming 10. Method of feasible directions 11. Frank-Wolfe Algorithm 12. Sequential Unconstrained Minimization Techniques (SUMT) 13. Geometric Programming
Lecture notes for this course are available. F.S. Hillier and G.J. Lieberman: Introduction to Operations Research, 8th Edition, McGraw-Hill, New York, 2005. M. Luptácik: Nichtlineare Programmierung mit ökonomischen Anwendungen, Athenäum, 1981. M. Luptácik: Mathematical Optimization and Economic Analysis, Springer edition, forthcoming.
