Characterizing efficiency without linear structure: a unified approach

DOI10.1007/s10898-007-9165-xzbMath1145.90063OpenAlexW2076390578MaRDI QIDQ933783

Elvira Hernández, Fabián Flores-Bazan, Vicente Novo Sanjurjo

Publication date: 25 July 2008

Published in: Journal of Global Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10898-007-9165-x

zbMATH Keywords

EfficiencyVector optimizationExistence resultsDomination propertySet optimization

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Set-valued maps in general topology (54C60) Programming in abstract spaces (90C48)

Related Items (18)

Efficiency in quasiconvex multiobjective nondifferentiable optimization on the real line ⋮ Optimality conditions for a unified vector optimization problem with not necessarily preordering relations ⋮ Variable preference relations: existence of maximal elements ⋮ On solutions of set-valued optimization problems ⋮ A Brézis-Browder principle on partially ordered spaces and related ordering theorems ⋮ Maximal elements under reference-dependent preferences with applications to behavioral traps and games ⋮ Existence of optimal points via improvement sets ⋮ A unified minimal solution in set optimization ⋮ Continuity and closedness of constraint and solution set mappings in unified parametric semi-infinite vector optimization ⋮ Qualitative properties of solutions to set optimization problems ⋮ Scalarizations for a unified vector optimization problem based on order representing and order preserving properties ⋮ Characterizing efficiency on infinite-dimensional commodity spaces with ordering cones having possibly empty interior ⋮ A new nonlinear scalarization function and applications ⋮ Some equivalent problems in set optimization ⋮ Essential stability in unified vector optimization ⋮ Existence and Convergence of Optimal Points with Respect to Improvement Sets ⋮ Continuity of solution maps to parametric set optimization problems via parametric equilibrium problems ⋮ Optimization problems for locally convex cone-valued functions

Cites Work

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• Pareto optimization in topological vector spaces
• An existence result for maximizations with respect to cones
• Nonconvex scalarization in set optimization with set-valued maps
• Existence and Lagrangian duality for maximization of set-valued functions
• Optimization and stability results through cone lower semicontinuity
• Comparison of existence results for efficient points
• Some variants of the Ekeland variational principle for a set-valued map
• Power structures
• Existence of efficient points in vector optimization and generalized Bishop-Phelps theorem
• Existence theorems for set optimization problems
• Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives
• An optimization result for set-valued mappings and a stability property in vector problems with constraints
• Set-relations and optimality conditions in set-valued maps
• Preferred answer sets for ordered logic programs
• Semi-Compactness with Respect to a Euclidean Cone
• On Cone-Efficiency, Cone-Convexity and Cone-Compactness
• An Existence Theorem in Vector Optimization
• Existence theorems of set optimization with set-valued maps

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