MMA0018 | Optimization techniques |
Teaching Staff in Charge |
Prof. LUPSA Liana, Ph.D., llupsamath.ubbcluj.ro Assoc.Prof. FINTA Zoltan, Ph.D., fzoltanmath.ubbcluj.ro |
Aims |
Presentation of certain topics concerning optimization problems and corresponding solving techniques of these problems.
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Content |
The notion of optimization problem. Models for interdisciplinary optimization problems.
Convex analysis in the euclidian n-dimensional space: convex sets, polyhedra, convex mappings; properties of convex mappings. Alternative theorems. The study of linear optimization problems; interpretation in economics; geometric interpretation; characterization of the existence/non-existence of solutions of a linear optimization problem. Techniques for solving linear optimization problems: the graphical method, the simplex method, the dual simplex method. Elements of game theory: solving matrix games by reducing them to linear optimization problems. Properties of minimum points of convex mappings; necessary and sufficient optimum conditions. |
References |
1. BLAGA, L., LUPŞA, L.: Elemente de programare liniară. Risoprint, Cluj-Napoca, 2003.
2. BLAGA, L., LUPŞA, L.: Cercetare operaţională. Argonaut, Cluj-Napoca, 2006. 3. BRECKNER, B.E.: De la poliedre la jocuri matriceale. O introducere in optimizarea liniara. EFES, Cluj-Napoca, 2007. 4. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003. 5. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operationala, EFES, Cluj-Napoca, 2006. 6. BRECKNER, W.W.: Cercetare operationala. Cluj-Napoca, Universitatea Babes-Bolyai, Fac. de Matematica, 1981. 7. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operaţională. Cluj-Napoca, Universitatea, Fac. de Matematica, 1983. 8. DOMSCHKE, W., DREXL, A.: Einfuhrung in Operations Research. 3. Aufl. Berlin, Springer-Verlag, 1995. 9. DOMSCHKE, W., DREXL, A., SCHILDT, B., SCHOLL, A., VOSS, S.: Uebungsbuch Operations Research. 2. Aufl. Berlin, Springer-Verlag, 1997. 10. PREKOPA, A.: Linearis programozas. Bolyai Tarsulat, Budapest, 1968. |
Assessment |
Continuous assessment (20% of the final grade), exam (written and oral), weighted with 80% of the final grade. |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |