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

Optimization theory
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MO016
8
2+2+0
7.5
optional
Matematică
MO016
8
2+2+0
8
optional
Matematică-Informatică
Teaching Staff in Charge
Assoc.Prof. KASSAY Gabor, Ph.D., kassay@math.ubbcluj.ro
Aims
To improve and broaden the students' knowledge developed within the course of Operations Research through the presentation of certain results and applications of the optimization theory developed in the framework of normed linear spaces. The course and seminar highlight at the same time, the role played by functional analysis in the study of certain problems of applied mathematics.
Content
Optimization on normed spaces. The existence and uniqueness of solutions. Generalized derivatives: Gateaux, Clarke. The cones of Clarke and Bouligand. Liusternik's theorem.
Necessary and sufficient conditions for the existence of optimal solutions. The generalized rule of multipliers. Duality theory in optimization. Minimax and saddlepoint theorems. Duality of linear and conic programming problems.
References
1. BAZARAA M. S., SHETTY C. M.: Foundations of optimization. Springer, Berlin, 1976.
2. GIRSANOV V.: Lectures on mathematical theory of extremum problems. Springer, Berlin, 1972.
3. JAHN J.: Introduction to the theory of nonlinear optimization. Springer, Berlin, 1994.
4. LAURENT P.-J.: Approximation et optimisation. Hermann, Paris, 1972.
5. SCHIROTZEK W.: Differenzierbare Extremalprobleme. BSB B. G. Teubner Verlagsges., Leipzig, 1989.
Assessment
Exam.