Vector Optimization |
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Teaching Staff in Charge |
Lect. 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. HILLERMEIER, C.: Nonlinear multiobjective optimization: a generalized homotopy approach. Birkhauser Verlag, Basel - Boston - Berlin, 2001.
2. JAHN, J.: Mathematical vector optimization in partially ordered linear spaces. Peter Lang Verlag, Frankfurt, 1986. 3. LUC, D.T.: Theory of vector optimization. Springer Verlag, Berlin, 1989. 4. SAWARAGI, Y., NAKAYAMA, H., TANINO, T.: Theory of Multiobjective Optimization. Academic Press, New York, 1985. 5. YU, P.L.: Multiple criteria decision making: concepts, techniques and extensions. Plenum Press, New York - London, 1985. 6. Articole de specialitate. |
Assessment |
Written and oral examination. |