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

Code	Subject	
MMA1008	Numerical Methods in Optimization	

Section	Sem.	Hours: C+S+L	Category	Type	
Mathematics	4	2+1+0	speciality	optional	

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	 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. JONGEN H.Th., MEER K., TRIESCH E.: Optimization Theory, New York, Boston, Dordrecht, London, Moscow: Kluwer Academic Publishers, 2004
6. LUPSA L.: Numerical optimization methods. Special issues in discrete optimization. Cluj-Napoca: Risoprint, 2005
7. NOCEDAL J., WRIGHT S.J.: Numerical Optimization, Second Edition, New York: Springer, 2006
8. PADBERG M.: Linear Optimization and Extensions, Springer-Verlag,Berlin, 1995
9. PANIK M.J.: Linear Programming: mathematics, theory and algorithms, Kluwer Academic Publishers, Dordrecht, 1996.
10. VOSE M.D., The simple Genetic Algorithm: Foundations and Theory. Cambrige: MIT Press,MA, 1998
	
Assessment	Exam and Prezentation.