"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science
| Special Topics in Modern Mathematics (2) |
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| Teaching Staff in Charge |
Prof. DUCA Dorel, Ph.D., dduca math.ubbcluj.ro |
| Aims |
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Students will learn the methods and techniques of optimization theory. |
| Content |
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1. Convex Analysis in Complex Space
1.1 Convex Sets 1.2 Separation Theorems for Convex Sets 1.3 Cones 1.4 The Polar of a Set 1.5 Theorems of the Alternative 1.6 Convex Functions and Generalizations of Convex Functions 2. Optimization in Complex Space 2.1 Optimization Problems in Complex Space 2.2 Necessary Optimality Criteria and Sufficient Optimality Criteria 2.3 Necessary Optimality Criteria with Differentiable Hypotheses about the Functions 2.4 Sufficient Optimality Criteria with Differentiable Hypotheses about the Functions 2.5 Linearization Properties of the Optimization Problem 3. Multicriteria Optimization in Complex Space 3.1 Efficient Points, Weakly Efficient Points, Ideal Points 3.2 The Structure of the Set of Efficient Points 3.3 Multicriteria Optimization Problems in Complex Space 3.4 Necessary Efficieny Criteria 3.5 Sufficient Efficiency Criteria 3.6 Properly Efficiency in the Multicriteria Optimization |
| References |
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1. J.-P. AUBIN: Optima and Equilibria. An Introduction to Nonlinear Analysis, Springer-Verlag, Berlin/Heidelberg 1993
2. J.-P. AUBIN and I. EKELAND: Applied Nonlinear Analysis, John Wiley and Sons, New York, 1984 3. D.I. DUCA: Multicriteria Optimization in Complex Space, Casa Cartii de Stiinta, Cluj-Napoca, 2005 4. D.I. DUCA: Optimization in Complex Space (in romanian), Ed. GIL, Zalau, 2002 5. C. ZALINESCU: Programare matematica in spatii normate infinit dimensionale, Ed. Academiei Romane, Bucuresti, 1998 |
| Assessment |
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Homeworks. Essays. Exam. |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |