Characterization of Approximate Solutions of Vector Optimization Problems with a Variable Order Structure

Behnam Soleimani ()
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Behnam Soleimani: Martin-Luther-University Halle-Wittenberg

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 2, No 15, 605-632

Abstract: Abstract In this paper, we deal with approximate solutions in vector-optimization problems with respect to a variable order structure. In the case of exact solutions of a vector optimization problem, especially in the variable order case, authors use a cone or a pointed convex cone-valued map in order to describe the solution concepts but in this paper, we use a set-valued map and this map is not a (pointed convex) cone-valued map necessarily. We characterize these solution concepts by a general scalarization method by means of nonlinear functionals. In the last section, an extension of Ekeland’s variational principle for a vector optimization problem with a variable order structure is given.

Keywords: Vector optimization; Variable order structure; Approximate solutions; Ekeland’s variational principle; 65k10; 90C29; 90C30; 90C48 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-014-0535-5

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