Nonlinear scalarization functions and polar cone in set optimization

DOI10.1007/s11590-016-1027-3zbMath1393.90109OpenAlexW2301626379MaRDI QIDQ519769

S. Khoshkhabar-amiranloo, Esmaile Khorram, Majid Soleimani-damaneh

Publication date: 5 April 2017

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-016-1027-3

zbMATH Keywords

nonlinear scalarizationset optimizationGerstewitz's functioncone-convex functionscone-quasiconvex functionspolar coneset solutions

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29)

Related Items (6)

Approximate weak minimal solutions of set-valued optimization problems ⋮ A calculation approach to scalarization for polyhedral sets by means of set relations ⋮ Scalarization of multiobjective robust optimization problems ⋮ A set scalarization function based on the oriented distance and relations with other set scalarizations ⋮ Stability of minimal solutions to parametric set optimization problems ⋮ Six set scalarizations based on the oriented distance: properties and application to set optimization

Cites Work

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• Vectorization in set optimization
• Pointwise well-posedness in set optimization with cone proper sets
• New nonlinear scalarization functions and applications
• On optimization problems with set-valued objective maps: existence and optimality
• Variational analysis of directional minimal time functions and applications to location problems
• New order relations in set optimization
• Nonconvex separation theorems and some applications in vector optimization
• On solutions of set-valued optimization problems
• Scalarization of set-valued optimization problems and variational inequalities in topological vector spaces
• Nonconvex scalarization in set optimization with set-valued maps
• Well-posedness for set optimization problems
• Existence and Lagrangian duality for maximization of set-valued functions
• Optimality conditions for set-valued optimization problems
• Variational methods in partially ordered spaces
• Some variants of the Ekeland variational principle for a set-valued map
• Lagrange multipliers for set-valued optimization problems associated with coderivatives
• Scalar characterizations of weakly cone-convex and weakly cone-quasiconvex functions
• On cone convexity of set-valued maps
• Set-valued analysis

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