SUBJECT
Title
Continuous optimization
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
3+3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
A short description of the course: Linear inequality systems: Farkas lemma and other alternative theorems, The duality theorem of linear programming, Pivot algorithms (criss-cross, simplex), Interior point methods, Matrix games: Nash equilibrium, Neumann theorem on the existence of mixed equilibrium, Convex optimization: duality, separability, Convex Farkas theorem, Kuhn-Tucker-Karush theorem, Nonlinear programming models, Stochastic programming models.
Readings
- Katta G. Murty: Linear Programming. John Wiley & Sons, New York, 1983.
- Vašek Chvátal: Linear Programming. W. H. Freeman and Company, New York, 1983.
- C. Roos, T. Terlaky and J.-Ph. Vial: Theory and Algorithms for Linear Optimization: An Interior Point Approach. John Wiley & Sons, New York, 1997.
- Béla Martos: Nonlinear Programming: Theory and Methods. Akadémiai Kiadó, Budapest, 1975.
- M. S. Bazaraa, H. D. Sherali and C. M. Shetty: Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York, 1993.
- J.-B. Hiriart-Urruty and C. Lemaréchal: Convex Analysis and Minimization Algorithms I-II. Springer-Verlag, Berlin, 1993.