A certified model reduction approach for robust parameter optimization with PDE constraints

DOI10.1007/s10444-018-9653-1zbMath1477.35291arXiv1703.01613OpenAlexW2909844392WikidataQ128596212 ScholiaQ128596212MaRDI QIDQ2000521

Michael Hinze, Stefan Ulbrich, Philip Kolvenbach, Oliver Lass, Alessandro Alla

Publication date: 28 June 2019

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.01613

zbMATH Keywords

proper orthogonal decompositionrobust optimizationparameter optimizationmodel order reduction

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Numerical optimization and variational techniques (65K10) Control/observation systems governed by partial differential equations (93C20) Existence of solutions for minimax problems (49J35) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical methods for partial differential equations, boundary value problems (65N99) PDEs in connection with control and optimization (35Q93) PDE constrained optimization (numerical aspects) (49M41)

Related Items

A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems, An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization, Consistency of Monte Carlo estimators for risk-neutral PDE-constrained optimization, Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs, Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters, Sampling-free model reduction of systems with low-rank parameterization, A space-time certified reduced basis method for quasilinear parabolic partial differential equations, Reduced Basis Methods for Quasilinear Elliptic PDEs with Applications to Permanent Magnet Synchronous Motors

Cites Work

• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• General robust-optimization formulation for nonlinear programming
• Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations
• Adjustable robust solutions of uncertain linear programs
• Robust optimization-methodology and applications
• Certified PDE-constrained parameter optimization using reduced basis surrogate models for evolution problems
• Nonlinear robust optimization via sequential convex bilevel programming
• An approximation technique for robust nonlinear optimization
• Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization
• A polynomial chaos meta‐model for non‐linear stochastic magnet variations
• Theory and Applications of Robust Optimization
• Complementarity constraints as nonlinear equations: Theory and numerical experience
• Optimization with PDE Constraints
• Introduction to Stochastic Programming
• Trust Region Methods
• Optimal Control of Stochastic Partial Differential Equations
• Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
• Local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition
• Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations
• A Certified Trust Region Reduced Basis Approach to PDE-Constrained Optimization
• Reduced basis method for finite volume approximations of parametrized linear evolution equations
• Local Convergence of SQP Methods for Mathematical Programs with Equilibrium Constraints
• Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item