"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Nelinear optimization
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO038
6
2+2+0
6
compulsory
Matematica Economica
MO038
6
2+2+0
6
compulsory
Matematici Aplicate
Teaching Staff in Charge
Lect. POPOVICI Nicolae, Ph.D., popovici@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.
References
1. Breckner, W. W.: Cercetare operationala. Lito. Univ. "Babes-Bolyai", Cluj, 1981.
2. Breckner, W. W., Duca, D.: Culegere de probleme de cercetare operationala. Lito. Univ. "Babes-Bolyai", Cluj, 1983.
3. Jahn, J.: Introduction to the theory of nonlinear optimization. Springer, Berlin, 1994.
4. Karmanov, V.: Programmation mathematique. Editions Mir, Moscou, 1977.
5. Kosmol, P.: Optimierung und Approximation. Walter de Gruyter & Co., Berlin, 1991.
6. Stefanescu, A., Zidaroiu, C.: Cercetari operationale. Editura Didactica si Pedagogica, Bucuresti, 1981.
Assessment
Exam.