A hybrid semismooth quasi-Newton method for nonsmooth optimal control with PDEs

DOI10.1007/s11081-020-09523-wzbMath1480.49026OpenAlexW3043796533WikidataQ114224235 ScholiaQ114224235MaRDI QIDQ2069115

Armin Rund, Florian Mannel

Publication date: 20 January 2022

Published in: Optimization and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11081-020-09523-w

zbMATH Keywords

quasi-Newton methodssuperlinear convergencesemismooth Newton methodsnonsmooth optimal controlBloch equations

Mathematics Subject Classification ID

Large-scale problems in mathematical programming (90C06) Applications of mathematical programming (90C90) Nonlinear programming (90C30) Derivative-free methods and methods using generalized derivatives (90C56) Optimality conditions for problems involving partial differential equations (49K20) Numerical methods based on necessary conditions (49M05) Newton-type methods (49M15) Nonsmooth analysis (49J52) Methods of quasi-Newton type (90C53) Software, source code, etc. for problems pertaining to calculus of variations and optimal control (49-04) Software, source code, etc. for problems pertaining to operations research and mathematical programming (90-04)

Related Items (7)

Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization ⋮ Consistency of Monte Carlo estimators for risk-neutral PDE-constrained optimization ⋮ Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners ⋮ Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs ⋮ Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization ⋮ Unnamed Item ⋮ OPTE special issue on PDE-constrained optimization

Cites Work

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• A semismooth Newton method for a class of semilinear optimal control problems with box and volume constraints
• A globally and superlinearly convergent quasi-Newton method for general box constrained variational inequalities without smoothing approximation
• Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
• On the convergence of some quasi-Newton methods for nonlinear equations with nondifferentiable operators
• Representations of quasi-Newton matrices and their use in limited memory methods
• Newton and quasi-Newton methods for normal maps with polyhedral sets
• A regularized semi-smooth Newton method with projection steps for composite convex programs
• Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach
• Semismooth Newton and quasi-Newton methods in weighted ℓ¹-regularization
• Directional Sparsity in Optimal Control of Partial Differential Equations
• Numerical PDE-Constrained Optimization
• Erratum: Directional Sparsity In Optimal Control of Partial Differential Equations
• Computational Optimization of Systems Governed by Partial Differential Equations
• A Simplified Approach to Semismooth Newton Methods in Function Space
• Lagrange Multiplier Approach to Variational Problems and Applications
• Optimization with PDE Constraints
• The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
• Convergence Rates of Quasi-Newton Algorithms for Some Nonsmooth Optimization Problems
• The Local Convergence of Broyden-Like Methods on Lipschitzian Problems in Hilbert Spaces
• Normal Maps Induced by Linear Transformations
• Newton and Quasi-Newton Methods for a Class of Nonsmooth Equations and Related Problems
• Semismooth Karush-Kuhn-Tucker Equations and Convergence Analysis of Newton and Quasi-Newton Methods for Solving these Equations
• An Introduction to Variational Inequalities and Their Applications
• Second Order Methods for Optimal Control of Time-Dependent Fluid Flow
• Sparse Optimal Control of the KdV-Burgers Equation on a Bounded Domain
• First-Order Methods in Optimization
• Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
• Optimal Control of Semilinear Parabolic Equations by BV-Functions
• Convex analysis and monotone operator theory in Hilbert spaces

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