Sequential characterization of solutions in convex composite programming and applications to vector optimization

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October 2008, 4(4): 767-782. doi: 10.3934/jimo.2008.4.767

Sequential characterization of solutions in convex composite programming and applications to vector optimization

Radu Ioan Boţ ^1, , Anca Grad ^2, and Gert Wanka ^1,

1.	Faculty of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany, Germany
2.	Faculty of Mathematics and Computer Sciences, Babeş-Bolyai University, Cluj-Napoca, 1 Kogãlniceanu Str., 400084 Cluj-Napoca, Romania

Received October 2007 Revised June 2008 Published October 2008

Abstract
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When characterizing optimal solutions of both scalar and vector optimization problems usually constraint qualifications have to be satisfied. By considering sequential characterizations, given for the first time in vector optimization in this paper, this drawback is eliminated. In order to establish them we give first of all sequential characterizations for a convex composed optimization problem with geometric and cone constraints. Then, by means of scalarization, we extend them to the vector case. For exemplification we particularize the characterization in the case of linear and set scalarization.

Keywords: sequential optimality conditions., properly and weakly efficient solutions, Convex vector optimization, scalarization.

Mathematics Subject Classification: Primary: 90C25, 90C29, 49K99; Secondary: 90C4.

Citation: Radu Ioan Boţ, Anca Grad, Gert Wanka. Sequential characterization of solutions in convex composite programming and applications to vector optimization. Journal of Industrial & Management Optimization, 2008, 4 (4) : 767-782. doi: 10.3934/jimo.2008.4.767

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