A calculus for set-valued maps and set-valued evolution equations

DOI10.1007/BF01025922zbMath0856.49016MaRDI QIDQ1900705

Zvi Artstein

Publication date: 4 February 1997

Published in: Set-Valued Analysis (Search for Journal in Brave)

zbMATH Keywords

set-valued mapsdifferential calculusnecessary conditions of optimalityset-valued differential equationscalculus of directivesmultiaffine mapping

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued functions (26E25) Set-valued maps in general topology (54C60) Nonlinear differential equations in abstract spaces (34G20) Set-valued and function-space-valued mappings on manifolds (58C06) Equations in function spaces; evolution equations (58D25)

Related Items (26)

Differential equations for closed sets in a Banach space, survey and extension ⋮ The Minkowski-Lyapunov equation ⋮ Weak solutions of set-valued stochastic differential equations ⋮ Algebraic and topological structure of some spaces of set-valued maps ⋮ On Fréchet differentiability of multifunctions ⋮ Stochastic set differential equations ⋮ Vector-valued interval functions and the Dedekind completion of \(C(X,E)\) ⋮ Stochastic inclusions and set-valued stochastic equations with mixed integrals in the plane ⋮ Fold-up derivatives of set-valued functions and the change-set problem: a survey ⋮ Semifixed sets of maps in hyperspaces with application to set differential equations ⋮ Second type Hukuhara differentiable solutions to the delay set-valued differential equations ⋮ Representations of affine multifunctions by affine selections ⋮ Expansion of Function with Uncertain Parameters in Higher Dimension ⋮ Interval Cauchy problem with a second type Hukuhara derivative ⋮ Differentiation of sets -- the general case ⋮ Control Minkowski-Lyapunov functions ⋮ The set of Hausdorff continuous functions -- the largest linear space of interval functions ⋮ A conversation with Estate V. Khmaladze ⋮ Differentiation of sets in measure ⋮ Existence of solutions for set differential equations involving causal operator with memory in Banach space ⋮ On connections between stochastic differential inclusions and set-valued stochastic differential equations driven by semimartingales ⋮ Stochastic integrals and stochastic equations in set-valued and fuzzy-valued frameworks ⋮ The \(s\)-differentiability of a fuzzy-valued mapping ⋮ Properties of set-valued integrals and set-valued stochastic equations driven by two-parameter martingales ⋮ Set-Valued Stochastic Integrals and Equations with Respect to Two-Parameter Martingales ⋮ Properties of set-valued stochastic differential equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some inverse mapping theorems
• On the set-valued calculus in problems of viability and control for dynamic processes: The evolution equation
• Conjugate derivative of a multivalued mapping and the differentiability of the maximum under connected constraints
• Proto-differentiability of set-valued mappings and its applications in optimization
• Piecewise linear approximations of set-valued maps
• On the differentiability of multifunctions
• Filippov and invariance theorems for mutational inclusions of tubes
• Shape Lyapunov functions and stabilization of reachable tubes of control problems
• First-order approximations for differential inclusions
• Mutational equations in metrics spaces
• On single-valuedness of convex set-valued maps
• On generalized dynamical systems defined by contingent equations
• Stability in general control systems
• Integrals of set-valued functions
• A differential calculus for multifunctions
• Trajectory integrals of set valued functions
• Local Controllability and Infinitesimal Generators of Semigroups of Set-Valued Maps
• Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
• Shape Sensitivity Analysis via Min Max Differentiability
• The Exponential Formula for the Reachable Set of a Lipschitz Differential Inclusion
• The eclipsing concept to approximate a multi-valued mapping
• Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian
• Difference Methods for Differential Inclusions: A Survey
• Inverse Function Theorems and Shape Optimization
• Sensitivity analysis for constraint and variational systems by means of set-valued differentiation

This page was built for publication: A calculus for set-valued maps and set-valued evolution equations