Subject: Numerical Methods in Optimization	Code: MO260	

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

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. 	
Selective References	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