Iterative Hard-Thresholding Applied to Optimal Control Problems with $L^0(\Omega)$ Control Cost
From MaRDI portal
Publication:3119535
DOI10.1137/18M1194602zbMath1410.49011arXiv1806.00297MaRDI QIDQ3119535
Publication date: 12 March 2019
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1806.00297
Optimality conditions for problems involving partial differential equations (49K20) Methods involving semicontinuity and convergence; relaxation (49J45) Discrete approximations in optimal control (49M25)
Related Items (11)
Sparse optimization problems in fractional order Sobolev spaces ⋮ Proximal algorithm for minimization problems in \(l_0\)-regularization for nonlinear inverse problems ⋮ Subdifferentiation of Nonconvex Sparsity-Promoting Functionals on Lebesgue Spaces ⋮ Optimality conditions, approximate stationarity, and applications – a story beyond lipschitzness ⋮ A Stabilized Sequential Quadratic Programming Method for Optimization Problems in Function Spaces ⋮ Integer optimal control problems with total variation regularization: Optimality conditions and fast solution of subproblems ⋮ Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisited ⋮ On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems ⋮ First and Second Order Conditions for Optimal Control Problems with an $L^0$ Term in the Cost Functional ⋮ A proximal gradient method for control problems with non-smooth and non-convex control cost ⋮ Computational inverse problems for partial differential equations. Abstracts from the workshop held December 6--12, 2020 (hybrid meeting)
Cites Work
- Characterization of maximum hands-off control
- Iterative hard thresholding methods for \(l_0\) regularized convex cone programming
- Multi-bang control of elliptic systems
- Iterative thresholding for sparse approximations
- Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
- A convex analysis approach to optimal controls with switching structure for partial differential equations
- Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms
- Directional Sparsity in Optimal Control of Partial Differential Equations
- Convergence and regularization results for optimal control problems with sparsity functional
- Pontryagin's Principle for State-Constrained Control Problems Governed by Parabolic Equations with Unbounded Controls
- Uniqueness of the maximal extension of a monotone operator
- An Extension of Pontryagin’s Principle for State-Constrained Optimal Control of Semilinear Elliptic Equations and Variational Inequalities
- Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with $L^1$ Cost Functional
- For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution
- Optimal Control with $L^p(\Omega)$, $p\in [0,1)$, Control Cost
- Convex analysis and monotone operator theory in Hilbert spaces
This page was built for publication: Iterative Hard-Thresholding Applied to Optimal Control Problems with $L^0(\Omega)$ Control Cost
