Second-order differentiability of generalized perturbation maps

DOI10.1007/s10898-011-9661-xzbMath1266.90179OpenAlexW2013729684MaRDI QIDQ421291

C. M. Liao, Sheng Jie Li

Publication date: 23 May 2012

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

Full work available at URL: https://doi.org/10.1007/s10898-011-9661-x

zbMATH Keywords

generalized equationgeneralized perturbation mapsecond-order lower semidifferentiabilitysecond-order proto-differentiabilitysecond-order semidifferentiability

Mathematics Subject Classification ID

Sensitivity, stability, parametric optimization (90C31)

Related Items (13)

On higher-order adjacent derivative of perturbation map in parametric vector optimization ⋮ On higher-order proto-differentiability and higher-order asymptotic proto-differentiability of weak perturbation maps in parametric vector optimization ⋮ Sensitivity analysis for set-valued equilibrium problems ⋮ Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions ⋮ On higher-order proto-differentiability of perturbation maps ⋮ On second-order proto-differentiability of perturbation maps ⋮ Some results on sensitivity analysis in set-valued optimization ⋮ Variational sets and asymptotic variational sets of proper perturbation map in parametric vector optimization ⋮ Generalized higher-order semi-derivative of the perturbation maps in vector optimization ⋮ Existence and boundedness of second-order Karush-Kuhn-Tucker multipliers for set-valued optimization with variable ordering structures ⋮ On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems ⋮ On set-valued optimization problems with variable ordering structure ⋮ On generalized second-order proto-differentiability of the benson proper perturbation maps in parametric vector optimization problems

Cites Work

• Unnamed Item
• Unnamed Item
• Calculus rules for derivatives of multimaps
• A method of duality for a mixed vector equilibrium problem
• On proto-differentiability of generalized perturbation maps
• Higher-order optimality conditions for set-valued optimization
• Are dualities appropriate for duality theories in optimization?
• Sensitivity of solutions to a parametric generalized equation
• Nonlinear analysis and variational problems. In Honor of George Isac
• Sensitivity analysis in multiobjective optimization
• Proto-differentiability of set-valued mappings and its applications in optimization
• Contingent derivative of the perturbation map in multiobjective optimization
• Second-order global optimality conditions for optimization problems
• Second-order optimality conditions in set optimization
• Implicit multifunction theorems for the sensitivity analysis of variational conditions
• On sensitivity analysis in vector optimization
• Contingent derivatives of set-valued maps and applications to vector optimization
• Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
• First and second order optimality conditions in set optimization
• Sensitivity Analysis of Solutions to Generalized Equations
• Variational Analysis
• Sensitivity of Solutions to Variational Inequalities on Banach Spaces
• Set-valued analysis

This page was built for publication: Second-order differentiability of generalized perturbation maps