|Teaching Staff in Charge|
|Lect. POPOVICI Nicolae, Ph.D., popovicimath.ubbcluj.ro|
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.
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.|
1. BRECKNER, B.E., POPOVICI, N.: Probleme de analiza convexa in R^n. Casa Cartii de Stiinta, Cluj-Napoca, 2003.
2. GOPFERT, A., RIAHI, H., TAMMER, C., ZALINESCU, C.: Variational Methods in Partially Ordered Spaces. Springer-Verlag, New York, 2003
3. HILLERMEIER, C.: Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach. Birkhauser Verlag, Basel - Boston - Berlin, 2001.
4. JAHN, J.: Mathematical Vector Optimization in Partially Ordered Linear Spaces. Peter Lang Verlag, Frankfurt, 1986.
5. LUC, D.T.: Theory of Vector Optimization. Springer Verlag, Berlin, 1989.
6. POPOVICI, N.: Optimizare vectoriala, Casa Cartii de Stiinta, Cluj-Napoca, 2005.
7. SAWARAGI, Y., NAKAYAMA, H., TANINO, T.: Theory of Multiobjective Optimization. Academic Press, New York, 1985.
8. YU, P.L.: Multiple criteria decision making: concepts, techniques and extensions. Plenum Press, New York - London, 1985.
Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).
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