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

SUBJECT

Code
Subject
MMA0018 Optimization techniques
Section
Semester
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.,  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.
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