Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMA0018	Optimization techniques	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics	6	2+1+0	speciality	compulsory	
Mathematics and Computer Science	6	2+1+0	speciality	compulsory	
Applied Mathematics	6	2+1+0	speciality	compulsory	

Teaching Staff in Charge	Prof. LUPSA Liana, Ph.D., llupsa@math.ubbcluj.ro
Assoc.Prof. FINTA Zoltan, Ph.D., fzoltan@math.ubbcluj.ro	
Aims	Presentation of certain topics concerning optimization problems and corresponding solving techniques of these problems.
	
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.
	
Bibliography	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.