Application of a Vector-Valued Ekeland-Type Variational Principle for Deriving Optimality Conditions

G. Isac and C. Tammer
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G. Isac: Royal Military College of Canada
C. Tammer: Martin-Luther-University Halle-Wittenberg

Chapter Chapter 23 in Nonlinear Analysis and Variational Problems, 2010, pp 343-365 from Springer

Abstract: Abstract In order to show necessary conditions for approximate solutions of vector-valued optimization problems in general spaces, we introduce an axiomatic approach for a scalarization scheme. Several examples illustrate this scalarization scheme. Using an Ekeland-type variational principle by Isac [12] and suitable scalarization techniques, we prove the optimality conditions under different assumptions concerning the ordering cone and under certain differentiability assumptions for the objective function.

Keywords: Risk Measure; Convex Cone; Topological Vector Space; Vector Optimization Problem; Closed Convex Cone (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-0158-3_23

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DOI: 10.1007/978-1-4419-0158-3_23

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