Second-order optimality conditions for strict efficiency of constrained set-valued optimization

DOI10.1007/s10957-012-0076-8zbMath1268.90078OpenAlexW1981090351MaRDI QIDQ1935295

Xiao-bing Li, Sheng Jie Li, Sheng-kun Zhu

Publication date: 14 February 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-012-0076-8

zbMATH Keywords

optimality conditionsset-valued optimizationsecond-order derivativeasymptotic second-order contingent conesemidifferentiable

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

Related Items (12)

Strict efficiency conditions for nonsmooth optimization with inclusion constraint under Hölder directional metric subregularity ⋮ Sharp efficiency for vector equilibrium problems on Banach spaces ⋮ New higher-order strong Karush-Kuhn-Tucker conditions for proper solutions in nonsmooth optimization ⋮ On necessary optimality conditions with higher-order complementarity slackness for set-valued optimization problems ⋮ On second-order proto-differentiability of perturbation maps ⋮ Strong Fermat rules for constrained set-valued optimization problems on Banach spaces ⋮ Second-order optimality conditions with the envelope-like effect for set-valued optimization ⋮ Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization ⋮ New set-valued directional derivatives: calculus and optimality conditions ⋮ Higher-Order Karush--Kuhn--Tucker Conditions in Nonsmooth Optimization ⋮ Optimality conditions for vector optimization problems with difference of convex maps ⋮ Second-order conditions for open-cone minimizers and firm minimizers in set-valued optimization subject to mixed constraints

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• New order relations in set optimization
• Second-order conditions for nonsmooth multiobjective optimization problems with inclusion constraints
• Higher order optimality conditions for Henig efficient solutions in set-valued optimization
• Higher-order optimality conditions for set-valued optimization
• New second-order directional derivative and optimality conditions in scalar and vector optimization
• Some variants of the Ekeland variational principle for a set-valued map
• Second-order optimality conditions in set optimization
• Optimality conditions in differentiable vector optimization via second-order tangent sets
• Lagrangian duality in set-valued optimization
• Set-relations and optimality conditions in set-valued maps
• \((\Lambda ,C)\)-contingent derivatives of set-valued maps
• Second order optimality conditions for differentiable multiobjective problems
• Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
• Higher-order necessary and sufficient conditions for strict local pareto minima in terms of Studniarski's derivatives
• Strict Efficiency in Set-Valued Optimization
• Necessary and Sufficient Conditions for Isolated Local Minima of Nonsmooth Functions
• Second-Order Conditions for Optimization Problems with Constraints
• A multiplier rule in set-valued optimisation
• The Lagrange Multiplier Rule in Set-Valued Optimization
• Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
• GENERALIZED CONTINGENT EPIDERIVATIVES IN SET-VALUED OPTIMIZATION: OPTIMALITY CONDITIONS
• Optimality conditions for maximizations of set-valued functions
• Set-valued analysis
• Strict efficiency in vector optimization

This page was built for publication: Second-order optimality conditions for strict efficiency of constrained set-valued optimization