Formulation of static optimization problems as nonlinear programming models, learning of theoretical knowledge and several solution techniques for the application of nonlinear programming in particular to economic problems.

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

written and oral The access to the concluding oral part of the exam requires a positive evaluation of the preceding written part of the exam.

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.