MMA0014 | Vector Optimization |
Teaching Staff in Charge |
Lect. POPOVICI Nicolae, Ph.D., popovicimath.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.: 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. |
Assessment |
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 |