Sensitivity Analysis and Optimal Control of Obstacle-Type Evolution Variational Inequalities

DOI10.1137/18M1183662zbMath1408.35094WikidataQ128563694 ScholiaQ128563694MaRDI QIDQ4610444

Constantin Christof

Publication date: 16 January 2019

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

zbMATH Keywords

optimal controlsensitivity analysisSignorini problemevolution variational inequalityparabolic obstacle problemstrong stationarityHadamard directional differentiability

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Sensitivity, stability, parametric optimization (90C31) Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators (35K85) Programming in abstract spaces (90C48) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (16)

On the nonuniqueness and instability of solutions of tracking-type optimal control problems ⋮ Lipschitz Stability and Hadamard Directional Differentiability for Elliptic and Parabolic Obstacle-Type Quasi-variational Inequalities ⋮ Stability and Sensitivity Analysis for Quasi-Variational Inequalities ⋮ Existence, iteration procedures and directional differentiability for parabolic QVIs ⋮ Optimal feedback control results for a second-order evolution system with finite delay ⋮ Strong stationarity for optimal control problems with non-smooth integral equation constraints: application to a continuous DNN ⋮ Existence, uniqueness, and stabilization results for parabolic variational inequalities ⋮ Optimization of a prey-predator model with hysteresis and convection ⋮ Strong Stationarity Conditions for Optimal Control Problems Governed by a Rate-Independent Evolution Variational Inequality ⋮ A Gauss--Seidel Type Method for Dynamic Nonlinear Complementarity Problems ⋮ Strong Stationarity for Optimal Control of a Nonsmooth Coupled System: Application to a Viscous Evolutionary Variational Inequality Coupled with an Elliptic PDE ⋮ On the differential variational inequalities of parabolic-parabolic type ⋮ Computation of a Bouligand Generalized Derivative for the Solution Operator of the Obstacle Problem ⋮ New regularity results and finite element error estimates for a class of parabolic optimal control problems with pointwise state constraints ⋮ Newton and Bouligand derivatives of the scalar play and stop operator ⋮ Solvability and pullback attractor for a class of differential hemivariational inequalities with its applications

Cites Work

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• Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the second kind
• Continuity in the parameter of the minimum value of an integral functional over the solutions of an evolution control system
• Hitchhiker's guide to the fractional Sobolev spaces
• Optimal control of parabolic 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
• A trust region algorithm for minimization of locally Lipschitzian functions
• Conical differentiability for evolution variational inequalities
• Optimal control of the obstacle for a parabolic variational inequality
• Global existence and Hadamard differentiability of hysteresis reaction-diffusion systems
• Optimal control of a non-smooth semilinear elliptic equation
• Directional differentiability for elliptic quasi-variational inequalities of obstacle type
• Plasticity. Mathematical theory and numerical analysis.
• Optimal control of ODE systems involving a rate independent variational inequality
• A new fully nonisothermal coupled model for the simulation of ice sheet flow
• Differential sensitivity analysis of variational inequalities with locally Lipschitz continuous solution operators
• On the directional differentiability of the solution mapping for a class of variational inequalities of the second kind
• Parabolic variational inequalities: the Lagrange multiplier approach
• Mathematical Models in Contact Mechanics
• Variational Stability of Some Optimal Control Problems Describing Hysteresis Effects
• The regularity of the positive part of functions in $L^2(I; H^1(\Omega)) \cap H^1(I; H^1(\Omega)^*)$ with applications to parabolic equations
• Optimal Control for Parabolic Variational Inequalities
• Steady, Shallow Ice Sheets as Obstacle Problems: Well-Posedness and Finite Element Approximation
• Variational Analysis in Sobolev andBVSpaces
• State Constrained Control Problems Governed by Variational Inequalities
• Necessary Conditions for Distributed Control Problems Governed by Parabolic Variational Inequalities
• On a Doubly Nonlinear Parabolic Obstacle Problem Modelling Ice Sheet Dynamics
• A Nonsmooth Trust-Region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities
• Sobolev Spaces on Metric Measure Spaces
• Optimal Control in Some Variational Inequalities
• Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints
• Optimal Control of Nonsmooth, Semilinear Parabolic Equations
• Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System
• Partial differential equations. An application-oriented introduction
• Stochastic differential equations. An introduction with applications.
• Tools for computational finance
• Comparison of optimality systems for the optimal control of the obstacle problem

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