Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MMA0014 | Vector Optimization |
| Teaching Staff in Charge |
Assoc.Prof. POPOVICI Nicolae, Ph.D., popovici math.ubbcluj.ro |
| Aims |
|
The aim of this course is to present some basic concepts and theoretical results of vector optimization and to apply them to the study of certain multicriteria optimization problems. |
| Content |
|
Convex analysis on partially ordered linear spaces; dual orderings; cone-convex sets; simply- and completely-shaded sets with respect to an ordering cone; cone-convex and cone-quasiconvex vector-valued functions. Vector optimization problems in general setting; concepts of optimality: strong-, weak-, proper-efficiency. Scalarization of vector optimization problems involving cone-convex or cone-quasiconvex objective functions. Necessary and/or sufficient conditions of efficiency for vector optimization problems. Geometrical and topological structure of efficient sets; existence of efficient solutions; connectedness and contractibility of efficient sets; approximation of efficient solutions. Applications to multicriteria optimization; best approximation in vectorial sense. |
| References |
|
1. BRECKNER, B.E., POPOVICI, N.: Convexity and Optimization. An Introduction, EFES, Cluj-Napoca, 2006.
2. EHRGOT, M.: Multicriteria Optimization. Springer, Berlin Heidelberg New York, 2005. 3. GOPFERT, A., RIAHI, H., TAMMER, C., ZALINESCU, C.: Variational Methods in Partially Ordered Spaces. Springer-Verlag, New York, 2003. 4. HILLERMEIER, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkhauser Verlag, Basel - Boston - Berlin, 2001. 5. JAHN, J.: Vector Optimization. Theory, Applications, and Extensions. Springer, Berlin, 2004. 6. LUC, D.T.: Theory of Vector Optimization. Springer Verlag, Berlin, 1989. 7. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005. |
| Assessment |
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Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment). |
| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |