Variational sets: calculus and applications to nonsmooth vector optimization

DOI10.1016/j.na.2010.11.039zbMath1211.49024OpenAlexW2050928938MaRDI QIDQ631705

Le Thanh Tung, Nguyen Le Hoang Anh, Phan Quoc Khanh

Publication date: 14 March 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.11.039

zbMATH Keywords

variational inequalitiesoptimality conditionsweak solutionssemi-compactnesscalculus ruleshigher-order variational sets of various kinds

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Set-valued and variational analysis (49J53)

Related Items (11)

Sensitivity analysis in constrained set-valued optimization via Studniarski derivatives ⋮ Variational sets of perturbation maps and applications to sensitivity analysis for constrained vector optimization ⋮ On sensitivity analysis of parametric set-valued equilibrium problems under the weak efficiency ⋮ Higher-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization with nonsolid ordering cones ⋮ Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization ⋮ On higher-order sensitivity analysis in nonsmooth vector optimization ⋮ On higher-order mixed duality in set-valued optimization ⋮ Higher-order optimality conditions and duality for approximate solutions in non-convex set-valued optimization ⋮ On Higher-Order Sensitivity Analysis of Parametric Henig Set-Valued Equilibrium Problems ⋮ Higher-order generalized tangent epiderivatives and applications to set-valued optimization ⋮ Higher-order optimality conditions for set-valued optimization with ordering cones having empty interior using variational sets

Cites Work

• Calculus rules for derivatives of multimaps
• Variational sets of multivalued mappings and a unified study of optimality conditions
• Higher-order variational sets and higher-order optimality conditions for proper efficiency in set-valued nonsmooth vector optimization
• Generalized differential calculus for nonsmooth and set-valued mappings
• Variational Analysis
• Some Calculus Rules for Contingent Epiderivatives

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