"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Optimization |
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| Teaching Staff in Charge |
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| Aims |
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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 |
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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 |
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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 |
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Exam. |