A convex analysis approach to optimal controls with switching structure for partial differential equations

DOI10.1051/cocv/2015017zbMath1338.49056arXiv1702.07540OpenAlexW3103782052WikidataQ57432534 ScholiaQ57432534MaRDI QIDQ2808060

Christian Clason, Kazufumi Ito, Karl Kunisch

Publication date: 26 May 2016

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.07540

zbMATH Keywords

optimal controlnonsmooth optimizationpartial differential equationsconvex relaxationswitching controlsemi-smooth Newton method

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical methods involving duality (49M29) Newton-type methods (49M15) Nonsmooth analysis (49J52) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical methods of relaxation type (49M20)

Related Items (16)

Characterization of maximum hands-off control ⋮ Convex Regularization of Discrete-Valued Inverse Problems ⋮ Vector-Valued Multibang Control of Differential Equations ⋮ Nonconvex penalization of switching control of partial differential equations ⋮ A convex analysis approach to multi-material topology optimization ⋮ Approximate moving horizon estimation for switching conservative linear infinite-dimensional systems ⋮ Sparse and switching infinite horizon optimal controls with mixed-norm penalizations ⋮ First and Second Order Conditions for Optimal Control Problems with an $L^0$ Term in the Cost Functional ⋮ Convex Relaxation of Discrete Vector-Valued Optimization Problems ⋮ Error estimates for the approximation of multibang control problems ⋮ \(L^1\) penalization of volumetric dose objectives in optimal control of PDEs ⋮ On an optimal control problem with gradient constraints ⋮ Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method ⋮ A Hybrid Finite-Dimensional RHC for Stabilization of Time-Varying Parabolic Equations ⋮ Coupled versus decoupled penalization of control complementarity constraints ⋮ Iterative Hard-Thresholding Applied to Optimal Control Problems with $L^0(\Omega)$ Control Cost

Cites Work

• Unnamed Item
• Unnamed Item
• Relaxation methods for mixed-integer optimal control of partial differential equations
• Robust null controllability for heat equations with unknown switching control mode
• Multi-bang control of elliptic systems
• Systems governed by ordinary differential equations with continuous, switching and impulse controls
• Switching control
• Nonsmooth analysis
• Optimal control of switched distributed parameter systems with spatially scheduled actuators
• Modeling and analysis of modal switching in networked transport systems
• Smoothing and First Order Methods: A Unified Framework
• Penalty Techniques for State Constrained Optimal Control Problems with the Wave Equation
• Lagrange Multiplier Approach to Variational Problems and Applications
• Optimal Switching for Ordinary Differential Equations
• Stabilization of the wave equation by on-off and positive-negative feedbacks
• Optimal switching boundary control of a string to rest in finite time
• Stability Criteria for Switched and Hybrid Systems
• Optimal Control with $L^p(\Omega)$, $p\in [0,1)$, Control Cost
• Proximité et dualité dans un espace hilbertien
• Perturbations of nonlinear maximal monotone sets in banach space
• Convex analysis and monotone operator theory in Hilbert spaces

This page was built for publication: A convex analysis approach to optimal controls with switching structure for partial differential equations