Optimal control and directional differentiability for elliptic quasi-variational inequalities

DOI10.1007/s11228-021-00624-xOpenAlexW3082125205WikidataQ114223368 ScholiaQ114223368MaRDI QIDQ2158825

Amal Alphonse, Carlos N. Rautenberg, Michael Hintermüller

Publication date: 26 July 2022

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

Full work available at URL: https://arxiv.org/abs/2008.13586

zbMATH Keywords

optimal controlsensitivity analysisobstacle problemdirectional differentiabilityquasi-variational inequalitystationarity conditions

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Derivatives of functions in infinite-dimensional spaces (46G05) Optimality conditions for problems involving relations other than differential equations (49K21) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (2)

Lipschitz Stability and Hadamard Directional Differentiability for Elliptic and Parabolic Obstacle-Type Quasi-variational Inequalities ⋮ Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

Cites Work

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• Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint
• Lakes and rivers in the landscape: a quasi-variational inequality approach
• Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints
• On a \(p\)-curl system arising in electromagnetism
• Numerical analysis of semilinear elliptic equations with finite spectral interaction
• Dirichlet forms and symmetric Markov processes.
• A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs
• Optimal control of a quasi-variational obstacle problem
• Equivalent complete norms and positivity
• Generalized Nash games and quasi-variational inequalities
• Banach lattices
• A uniqueness theorem for elliptic quasi-variational inequalities
• Contrôle dans les inéquations variationelles elliptiques
• How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities
• Regularity and stability for the mathematical programming problem in Banach spaces
• Optimal control of an obstacle problem
• Use of augmented Lagrangian methods for the optimal control of obstacle problems
• Directional differentiability for elliptic quasi-variational inequalities of obstacle type
• Variational and quasivariational inequalities with first order constraints
• Sur le contrôle optimal de systèmes distribués
• Parabolic quasi-variational diffusion problems with gradient constraints
• Analysis of a quasi-variational contact problem arising in thermoelasticity
• Elliptic quasi-variational inequalities under a smallness assumption: uniqueness, differential stability and optimal control
• Optimal control problems for quasi-variational inequalities and its numerical approximation
• Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
• Optimal control problems for certain quasivariational inequalities^∗
• Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
• Towards M-stationarity for Optimal Control of the Obstacle Problem with Control Constraints
• A quasi-variational inequality problem arising in the modeling of growing sandpiles
• Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities
• Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs
• First-Order Optimality Conditions for Elliptic Mathematical Programs with Equilibrium Constraints via Variational Analysis
• Recent Trends and Views on Elliptic Quasi-Variational Inequalities
• Coderivative Analysis of Quasi‐variational Inequalities with Applications to Stability and Optimization
• Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm
• A QUASI-VARIATIONAL INEQUALITY PROBLEM IN SUPERCONDUCTIVITY
• Mathematical methods of game and economic theory
• Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
• An elliptic quasi-variational inequality with gradient constraints and some of its applications
• An Introduction to Variational Inequalities and Their Applications
• Stability of the Solution Set of Quasi-variational Inequalities and Optimal Control
• Optimal Control in Some Variational Inequalities
• Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints
• Stationary Quasivariational Inequalities with Gradient Constraint and Nonhomogeneous Boundary Conditions
• Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints
• Smooth analysis in Banach spaces
• On the regularity of the solution of a variational inequality
• Nonlinear partial differential equations with applications
• Generalized Nash equilibrium problems
• Comparison of optimality systems for the optimal control of the obstacle problem

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