MMA0008 | Operations Research |
Teaching Staff in Charge |
Prof. LUPSA Liana, Ph.D., llupsamath.ubbcluj.ro Assoc.Prof. BRECKNER Brigitte Erika, Ph.D., brigittemath.ubbcluj.ro Assoc.Prof. FINTA Zoltan, Ph.D., fzoltanmath.ubbcluj.ro |
Aims |
This course is an introduction to operations research and to the mathematical theory of solving optimization problems. |
Content |
Operations research principles; interdisciplinary models. Convex analysis on the n-dimensional Euclidean space; convex sets; convex cones; alternative theorems; characterizations of convex and generalized convex functions. Constrained and unconstrained optimization problems; properties of minimum points of convex functions; necessary and sufficient optimality conditions; saddle-point theorems; duality theorems. Numerical methods for solving linear and nonlinear optimization problems: the Simplex method, the cutting planes method, penalty and barier functions methods. Introduction to game theory; the solution of two-persons games by means of linear optimization technique. |
References |
1. BLAGA, L., LUPSA, L.: Elemente de programare liniara. Risoprint, Cluj-Napoca, 2003.
2. BLAGA, L., LUPSA, L.: Cercetare operationala. 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 operaţională, 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 operationala. 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 evaluation (contributes 20% to the assesment), written and oral examination (contributes 80% to the assesment) |
Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |