Convex Relaxation of Discrete Vector-Valued Optimization Problems
DOI10.1137/21M1426237zbMath1476.49020arXiv2108.10077OpenAlexW3193511779MaRDI QIDQ5162643
Carla Tameling, Benedikt Wirth, Christian Clason
Publication date: 5 November 2021
Published in: SIAM Review (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2108.10077
linear elasticityconvex relaxationbranched transportsemismooth Newton methodBloch equationmultibang control
Convex programming (90C25) Sensitivity, stability, well-posedness (49K40) Newton-type methods (49M15) Biomedical imaging and signal processing (92C55) Classical linear elasticity (74B05) Methods involving semicontinuity and convergence; relaxation (49J45) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Existence theories for optimal control problems involving partial differential equations (49J20)
Cites Work
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- Multi-bang control of elliptic systems
- Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
- Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks
- Nonsmooth analysis
- Optimal transportation networks. Models and theory
- Optimal control of nonsmooth distributed parameter systems
- Numerical calibration of Steiner trees
- Error estimates for the approximation of multibang control problems
- Optimal control of the principal coefficient in a scalar wave equation
- Geometric and numerical methods in the contrast imaging problem in nuclear magnetic resonance
- Analysis of backtrack algorithms for listing all vertices and all faces of a convex polyhedron.
- A convex analysis approach to optimal controls with switching structure for partial differential equations
- A convex analysis approach to multi-material topology optimization
- Functional Analysis, Calculus of Variations and Optimal Control
- Lagrange Multiplier Approach to Variational Problems and Applications
- Optimization with PDE Constraints
- A Minimum Principle and a Generalized Bang-Bang-Principle for a Distributed Optimal Control Problem with Constraints on Control and State
- Convex Regularization of Discrete-Valued Inverse Problems
- Total variation regularization of multi-material topology optimization
- Optimality conditions and generalized bang—bang principle for a state—constrained semilinear parabolic problem
- Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with $L^1$ Cost Functional
- SPECT with a multi-bang assumption on attenuation
- A Multimaterial Transport Problem and its Convex Relaxation via Rectifiable $G$-currents
- Finite Elemente
- Efficient numerical solution of parabolic optimization problems by finite element methods
- Optimal Control with $L^p(\Omega)$, $p\in [0,1)$, Control Cost
- Convex analysis and monotone operator theory in Hilbert spaces
