|MMA1011||Mathematical Foundations of Decision-Making Process|
|Teaching Staff in Charge|
|Assoc.Prof. POPOVICI Nicolae, Ph.D., popovicimath.ubbcluj.ro|
The aim of the course is to introduce fundamental mathematical concepts and practical methods relevant to the study of decision-making processes as optimization problems.
Partial ordered sets; linear preorder relations and their characterizations in terms of ordering cones. Preference relations induced by utility functions; optimality concepts; decisional processes as scalar or vector optimization problems. Convex sets and polyhedral sets; extreme points; convex functions and the properties of their minimum points. Necessary and sufficient optimality conditions for unconstrained and constrained optimization problems. Saddle point theorems. Duality theorems in linear optimization. Numerical methods for solving optimization problems: the Simplex algorithm in primal and dual form, the cutting planes method. Conflict and competition problems, two-player matrix games and their solution by means of linear programming.|
1. ANDERSON, D.R., SWEENEY, D.J., WILLIAMS, T.A., An Introduction to Management Science. Quantitative Approaches to Decision Making, South-Western College Publishing, Cincinnati, 2000.
2. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operaţională, EFES, Cluj-Napoca, 2006.
3. BRECKNER, B.E., POPOVICI, N.: Convexity and Optimization. An Introduction, EFES, Cluj-Napoca, 2006.
4. BRECKNER, W.W.: Cercetare operationala, Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1981.
5. BRECKNER, W.W., DUCA, D.: Culegere de probleme de cercetare operationala, Universitatea $Babes-Bolyai$, Facultatea de Matematica, Cluj-Napoca, 1983.
6. EHRGOT, M.: Multicriteria Optimization, Springer, Berlin Heidelberg New York, 2005.
7. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
8. YU, P.L.: Multiple Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York - London, 1985.
Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).
|Links:||Syllabus for all subjects|
Romanian version for this subject
Rtf format for this subject