"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Operations research |
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| Teaching Staff in Charge |
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| Aims |
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This course is an introduction to operations research and to the mathematical theory of solving optimization problems. |
| Content |
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General principles of operations research; interdisciplinary models. Convex analysis on the n-dimensional Euclidean space; 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: Simplex method, 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 |
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1. BOYD, S., VANDENBERGHE, L.: Convex optimization. Cambridge University Press, Cambridge, 2004.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003. 3. BRECKNER, W.W.: Cercetare operationala. Cluj-Napoca, Universitatea "Babes-Bolyai", Fac. de Matematica, 1981. 4. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operationala. Cluj-Napoca, Universitatea, Fac. de Matematica, 1983. 5. DOMSCHKE, W., DREXL, A.: Einfuhrung in Operations Research. 3. Aufl. Berlin, Springer-Verlag, 1995. 6. DOMSCHKE, W., DREXL, A., SCHILDT, B., SCHOLL, A., VOSS, S.: Uebungsbuch Operations Research. 2. Aufl. Berlin, Springer-Verlag, 1997. 7. PREKOPA, A.: Linearis programozas. Bolyai Tarsulat, Budapest, 1968. |
| Assessment |
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Continuous evaluation (contributes 20% to the assesment), written and oral examination (contributes 80% to the assesment) |