Nonlinear Scalarizations of Set Optimization Problems with Set Orderings

DOI10.1007/978-3-662-48670-2_2zbMath1337.49025OpenAlexW2413329969MaRDI QIDQ2805753

Bienvenido Jiménez, César Gutiérrez, Vicente Novo Sanjurjo

Publication date: 13 May 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-48670-2_2

zbMATH Keywords

optimality conditionsnonlinear scalarizationset-valued optimizationset relationslocally convex topological linear space

Mathematics Subject Classification ID

Set-valued and variational analysis (49J53) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Optimality conditions for problems in abstract spaces (49K27)

Related Items (11)

Characterizations of the set less order relation in nonconvex set optimization ⋮ An unified scalarization and Ekeland's variational principle for partial set order ⋮ A set scalarization function based on the oriented distance and relations with other set scalarizations ⋮ Some properties of nonconvex oriented distance function and applications to vector optimization problems ⋮ Six set scalarizations based on the oriented distance: properties and application to set optimization ⋮ Characterization of set relations through extensions of the oriented distance ⋮ A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa's set approach ⋮ On Lagrange Multiplier Rules for Set-Valued Optimization Problems in the Sense of Set Criterion ⋮ Treatment of set order relations by means of a nonlinear scalarization functional: a full characterization ⋮ Existence of Lagrange multipliers for set optimization with application to vector equilibrium problems ⋮ Arcwise connected cone-quasiconvex set-valued mappings and Pareto reducibility in vector optimization

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• Some variants of the Ekeland variational principle for a set-valued map
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• Duality for Set-Valued Measures of Risk
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