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

Code	Subject	
MMA0006	Linear Optimization	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	5	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Lect. BRECKNER Brigitte Erika, Ph.D., brigitte@math.ubbcluj.ro	
Aims	The formulation of the primal and dual linear programming problem, the presentation of the primal and dual simplex algorithm, the study of some particular classes of linear programming problem, applications.
To know the main algorithms for solving these types of problems.	
Content	1. Mathematical models. The general formulation of the optimization problem: the particular case of the linear optimization problem.
2. Linear system of equations and inequations: polytopes and polyhedrals. Linear functions; affine functions; properties of the optimum points for affine functions. Farkas@s lemma.
3. The simplex algorithm.
4. The duality in linear programming; economical interpolations; the dual simplex algorithm. 
5. The study of the stability of the solution of a linear optimization problems. Reoptimizations. Parametrizations.
6. Linear stochastic optimization problems. 
7. The approximation of the solutions of linear incompatible systems.
8. Transportation problems: the determination of a transportation plan, the determination of an optimal plan.	
Bibliography	1) Blaga L., Lupsa L., Elemente de programare liniara. Cluj-Napoca: Ed. Risoprint, 2003
2) Blaga L., Lupsa L., Cercetare operationala. Cluj-Napoca: Ed. Argonaut, 2006.
3) Breckner W.W., Cercetare operationala. Cluj-Napoca: Universitatea "Babes-Bolyai", Facultatea de matematica, 1981.
4) Breckner W.W., Duca I. D., Culegere de probleme de cercetare operationala. Cluj-Napoca: Universitatea "Babes-Bolyai", Facultatea de Matematica si Informatica, 1983.
5) Goldstein E., Youdine D., Problemes particuliers de la programmation lineaire. Moscou: Editions Mir,1966.
6) Marusciac I. Programare matematica. Cluj-Napoca: Universitatea "Babes-Bolyai" Facultatea de Matematica, Catedra de analiza, 1975.
7) Stancu-Minasian I.M., Programarea stohastica cu mai multe functii obiectiv. Bucuresti: Ed. Academiei R.S.R., 1980.
8) Szabo Zs. K, Cercetari operationale. Optimizari liniare. Targu Mures: Ed. Universitatii Petru Maior, 2005.
9) Varga J., Angewandte optimierung. Budapest: Akademiai Kiado, 1991.
10) Zuhovitki S.I., Avdeeva L.I., Lineinoie i vypukloie programirovanie. Moskva: Izd. Nauka, 1964.	
Assessment	Project + Exam.