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

Code	Subject	
MMA0009	Nonlinear Optimization	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	6	2+2+0	speciality	compulsory	

Teaching Staff in Charge	Prof. MURESAN Marian, Ph.D., mmarian@math.ubbcluj.ro	
Aims	Students should be familiar with both theoretical foundation and numerical methods for solving unconstrained or constrained nonlinear mathematical programming problems, which arise in applied mathematics.	
Content	Convex analysis on the n-dimensional Euclidean space; properties of the minimum points of convex and generalized convex functions. Constrained optimization problems. Necessary and sufficient optimality conditions. Saddle point theorems. Duality of optimization problems. 
Numerical methods for solving nonlinear optimization problems: unidimensional optimization methods, descent methods for unconstrained optimization problems, penalty and barier methods for constrained optimization problems, other specifical methods for special classes of optimization problems.	
Bibliography	1. BOYD, S., VANDENBERGHE, L.: Convex Optimization. Cambridge University Press, Cambridge, 2004. 
2. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003.
3. BRECKNER, B.E., POPOVICI, N.: Probleme de cercetare operationala. Editura EFES, Cluj-Napoca, 2006.
4. BRECKNER, W. W.: Cercetare operationala. Lito. Univ. "Babes-Bolyai", Cluj, 1981.
5. BRECKNER, W. W., Duca, D.: Culegere de probleme de cercetare operationala. Lito. Univ. "Babes-Bolyai", Cluj, 1983.
6. JAHN, J.: Introduction to the Theory of Nonlinear Optimization. Springer, Berlin, 1994.
7. KARMANOV, V.: Programmation mathematique. Editions Mir, Moscou, 1977.
8. KOSMOL, P.: Optimierung und Approximation. Walter de Gruyter & Co., Berlin, 1991.
9. STEFANESCU, A., ZIDAROIU, C.: Cercetari operationale. Editura Didactica si Pedagogica, Bucuresti, 1981.
	
Assessment	Written and oral exam.