Vector Optimization 
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Teaching Staff in Charge 

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; coneconvex sets; simply and completelyshaded sets with respect to an ordering cone; coneconvex and conequasiconvex vectorvalued functions. Vector optimization problems in general setting; concepts of optimality: strong, weak, properefficiency. Scalarization of vector optimization problems involving coneconvex or conequasiconvex 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, ClujNapoca, 2003.
2. GOPFERT, A., RIAHI, H., TAMMER, C., ZALINESCU, C.: Variational methods in partially ordered spaces. SpringerVerlag, 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. SAWARAGI, Y., NAKAYAMA, H., TANINO, T.: Theory of Multiobjective Optimization. Academic Press, New York, 1985. 7. YU, P.L.: Multiple criteria decision making: concepts, techniques and extensions. Plenum Press, New York  London, 1985. 
Assessment 
Continuous evaluation and directed project works (contribute 25% to the assesment), mid term exam (written and oral; contributes 25% to the assesment), final exam (written and oral; contributes 50% to the assesment). 