Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MMA0014	Vector Optimization	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	6	2+1+0	speciality	optional	

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.	
Bibliography	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	Continuous evaluation (contributes 20% to the assesment), written and oral exam (contributes 80% to the assesment).