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

Code	Subject	
MO260	Numerical Methods in Optimization	

Section	Semester	Hours: C+S+L	Category	Type	
Real and Compex Analysis - in English	2	2+2+0		compulsory	

Teaching Staff in Charge	Prof. LUPSA Liana, Ph.D., llupsa@math.ubbcluj.ro	
Aims	Getting to know some significant numerical methods for solving the optimization problems.	
Content	1. Numerical methods to minimize the unimodal functions. 
2. Numerical methods to minimize the unconstrained function: decreasing methods, conjugated directions methods, relaxation methods, methods whithout the hypothesis of differentiability.
3. Numerical methods with feasible directions,
4 .Numerical methods based on reducing constrained problems to unconstrained ones
5. Cutting methods, 
6. Inner point methods 
7. Branch and bound methods.
8. Specific methods to solve fractional, hyperbolic and quadratic programming problems are studied, too.
9. Methods to solve liniar optimisation problems: simplex methods, Hacian's method, Karmarkar's method. 
	
Bibliography	1. ANDREI N., Programare matematica avansata. Teorie, metode computationale, aplicatii. Bucuresti: Ed. Tehnica, 1999.
2. BRECKNER W.W.: Cercetare operationala, Univ.Babes-Bolyai, Cluj-Napoca ,1981.
3. BRECKNER W.W., DUCA D.I.: Culegere de probleme de cercetare operationala, Universitatea, Cluj-Napoca, 1983.
4. FORGO F., Nonconvex programming. Budapest: Akademiai Kiado, 1988.
5. PADBERG M.: Linear Optimization and Extensions, Springer-Verlag,Berlin, 1995
6. PANIK M.J.: Linear Programming: mathematics, theory and algorithms, Kluwer Academic Publishers, Dordrecht, 1996.
7. VOSE M.D., The simple Genetic Algorithm: Foundations and Theory. Cambrige: MIT Press, MA, 1998.
	
Assessment	Project and Prezentation.