Optimality Conditions for Metrically Consistent Approximate Solutions in Vector Optimization

C. Gutiérrez, B. Jiménez and V. Novo ()
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C. Gutiérrez: Universidad de Valladolid
B. Jiménez: Universidad Nacional de Educación a Distancia
V. Novo: Universidad Nacional de Educación a Distancia

Journal of Optimization Theory and Applications, 2007, vol. 133, issue 1, No 4, 49-64

Abstract: Abstract In this paper, approximate solutions of vector optimization problems are analyzed via a metrically consistent ε-efficient concept. Several properties of the ε-efficient set are studied. By scalarization, necessary and sufficient conditions for approximate solutions of convex and nonconvex vector optimization problems are provided; a characterization is obtained via generalized Chebyshev norms, attaining the same precision in the vector problem as in the scalarization.

Keywords: Vector optimization; ε-Efficiency; Scalarization; Gauge functionals; Generalized Chebyshev norms (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9191-3

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