Calculus rules for derivatives of multimaps
From MaRDI portal
Publication:833013
DOI10.1007/s11228-009-0105-4zbMath1173.54008OpenAlexW4300292049MaRDI QIDQ833013
Jean-Paul Penot, Sheng Jie Li, Kaiwen Meng
Publication date: 11 August 2009
Published in: Set-Valued and Variational Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11228-009-0105-4
calmnesscontingent derivative: incident derivativeproto-differentiabilitysemi-differentiabilityupper Lipschitz property
Nonsmooth analysis (49J52) Set-valued maps in general topology (54C60) Hyperspaces in general topology (54B20) Set-valued operators (47H04)
Related Items (23)
Higher-order set-valued Hadamard directional derivatives: calculus rules and sensitivity analysis of equilibrium problems and generalized equations ⋮ Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions ⋮ On sensitivity analysis of parametric set-valued equilibrium problems under the weak efficiency ⋮ Higher-order tangent derivative and its applications to sensitivity analysis ⋮ Higher-order Karush-Kuhn-Tucker optimality conditions for set-valued optimization with nonsolid ordering cones ⋮ New set-valued directional derivatives: calculus and optimality conditions ⋮ Second-order differentiability of generalized perturbation maps ⋮ Variational sets: calculus and applications to nonsmooth vector optimization ⋮ Second-order contingent derivatives of set-valued mappings with application to set-valued optimization ⋮ Scalar Lagrange multiplier rules for set-valued problems in infinite-dimensional spaces ⋮ Higher-order radial derivatives and optimality conditions in nonsmooth vector optimization ⋮ Expansion of Function with Uncertain Parameters in Higher Dimension ⋮ On higher-order mixed duality in set-valued optimization ⋮ Coderivatives of the generalized perturbation maps ⋮ Generalized second-order contingent epiderivatives in parametric vector optimization problems ⋮ Metric inequality conditions on sets and consequences in optimization ⋮ Calculus rules of the generalized contingent derivative and applications to set-valued optimization ⋮ Codifferential calculus ⋮ Second-order composed contingent derivatives of perturbation maps in set-valued optimization ⋮ On set-valued optimization problems with variable ordering structure ⋮ Expansion of Generalized Hukuhara Differentiable Interval Valued Function ⋮ On optimality conditions for set-valued equilibrium problems ⋮ Higher-order optimality conditions for set-valued optimization with ordering cones having empty interior using variational sets
Cites Work
- Unnamed Item
- Compact nets, filters, and relations
- On proto-differentiability of generalized perturbation maps
- Proto-differentiability of set-valued mappings and its applications in optimization
- Contingent derivative of the perturbation map in multiobjective optimization
- Sensitivity analysis for nonsmooth generalized equations
- Nonsingularity conditions for multifunctions
- Lipschitzian inverse functions, directional derivatives, and applications in \(C^{1,1}\) optimization
- Continuity of usual operations and variational convergences
- Implicit multifunction theorems for the sensitivity analysis of variational conditions
- Lipschitzian Multifunctions and a Lipschitzian Inverse Mapping Theorem
- Tangent Cones and Quasi-Interiorly Tangent Cones to Multifunctions
- Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
- An Implicit-Function Theorem for a Class of Nonsmooth Functions
- Generalized Gradients and Applications
- Variational Analysis
- On the Calmness of a Class of Multifunctions
- On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems
- Metric regularity: characterizations, nonsmooth variations and successive approximation∗
This page was built for publication: Calculus rules for derivatives of multimaps
