Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization

DOI10.1007/s00186-020-00736-4OpenAlexW3122781822MaRDI QIDQ2040433

A. Vílchez, Vicente Novo Sanjurjo, Bienvenido Jiménez, Lidia Huerga

Publication date: 14 July 2021

Published in: Mathematical Methods of Operations Research (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00186-020-00736-4

zbMATH Keywords

Lagrange multiplierscontinuityconvexityset optimizationset order relationsoriented distancescalarization in set optimization

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Set-valued and variational analysis (49J53) Generalizations of ordered sets (06A75)

Related Items (5)

A new scalarization approach and applications in set optimization ⋮ A note on ``Levitin-Polyak well-posedness in set optimization concerning Pareto efficiency ⋮ Connectedness of the solution sets in generalized semi-infinite set optimization ⋮ Directional and approximate efficiency in set optimization ⋮ New notions of proper efficiency in set optimization with the set criterion

Cites Work

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• Four types of nonlinear scalarizations and some applications in set optimization
• New order relations in set optimization
• Nonconvex separation theorems and some applications in vector optimization
• Nonconvex scalarization in set optimization with set-valued maps
• Lagrange multipliers for \(\varepsilon \)-Pareto solutions in vector optimization with nonsolid cones in Banach spaces
• Analysis II. Convex analysis and approximation theory. Transl. from the Russian by D. Newton
• Variational methods in partially ordered spaces
• Relationships between the oriented distance functional and a nonlinear separation functional
• Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications
• Continuity of cone-convex functions
• Scalarization in set optimization with solid and nonsolid ordering cones
• Characterization of set relations through extensions of the oriented distance
• A unified characterization of nonlinear scalarizing functionals in optimization
• First-order optimality conditions in set-valued optimization
• Lagrange multipliers for set-valued optimization problems associated with coderivatives
• A new nonlinear scalarization function and applications
• A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization
• Duality for Set-Valued Measures of Risk
• Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
• Degrees of Efficiency and Degrees of Minimality
• Characterizations of set relations with respect to variable domination structures via oriented distance function
• Characterizations of set order relations and constrained set optimization problems via oriented distance function
• A set scalarization function based on the oriented distance and relations with other set scalarizations
• Six set scalarizations based on the oriented distance: properties and application to set optimization
• Nonlinear scalarizing functions in set optimization problems
• Some useful set-valued maps in set optimization
• Set-valued Optimization

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