Vectorization of set-valued maps with respect to total ordering cones and its applications to set-valued optimization problems

DOI10.1016/j.jmaa.2011.06.045zbMath1225.90117OpenAlexW2032060404MaRDI QIDQ641583

İlknur Atasever, Yalçın Küçük, Mustafa Soyertem, Küçük, Mahide

Publication date: 24 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.06.045

zbMATH Keywords

scalarizationtotal ordervectorizationset-valued optimizationsuccessive weighted sum methodweighted sum method

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29)

Related Items (7)

Partial order relations on family of sets and scalarizations for set optimization ⋮ Approximate solutions for set optimization with an order cone that has nonempty quasirelative interiors ⋮ A lexicographical order induced by Schauder bases ⋮ A vectorization for nonconvex set-valued optimization ⋮ Some optimality criteria of interval programming problems ⋮ Scalar representation and conjugation of set-valued functions ⋮ The generalization of total ordering cones and vectorization to separable Hilbert spaces

Cites Work

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• On constructing total orders and solving vector optimization problems with total orders
• Pareto optimality, game theory and equilibria
• Existence theorems in vector optimization
• Optimality conditions for set-valued optimization problems
• A survey of recent developments in multiobjective optimization
• Handbook of multicriteria analysis
• On the Scalarization of Set-Valued Optimization Problems with Respect to Total Ordering Cones
• Multicriteria Optimization

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