An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty
From MaRDI portal
Publication:2071422
DOI10.1007/s11081-018-9388-3OpenAlexW2805586941WikidataQ129713225 ScholiaQ129713225MaRDI QIDQ2071422
Stefan Ulbrich, Philip Kolvenbach, Oliver Lass
Publication date: 28 January 2022
Published in: Optimization and Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11081-018-9388-3
Optimality conditions for problems involving partial differential equations (49K20) Optimality conditions for minimax problems (49K35) PDEs in connection with mechanics of deformable solids (35Q74) Geometrical methods for optimization problems in solid mechanics (74P20)
Related Items
A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems, A survey of nonlinear robust optimization, A variational inequality based stochastic approximation for estimating the flexural rigidity in random fourth-order models, Optimality Conditions and Moreau–Yosida Regularization for Almost Sure State Constraints, An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization, Consistency of Monte Carlo estimators for risk-neutral PDE-constrained optimization, Performance Bounds for PDE-Constrained Optimization under Uncertainty, An Approximation Scheme for Distributionally Robust Nonlinear Optimization, An Interior-Point Approach for Solving Risk-Averse PDE-Constrained Optimization Problems with Coherent Risk Measures, Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters, An introduction to partial differential equations constrained optimization, A regularized stochastic subgradient projection method for an optimal control problem in a stochastic partial differential equation
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On fast trust region methods for quadratic models with linear constraints
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- Selected topics in robust convex optimization
- General robust-optimization formulation for nonlinear programming
- A semidefinite framework for trust region subproblems with applications to large scale minimization
- Robust solutions of linear programming problems contaminated with uncertain data
- Robust optimization-methodology and applications
- UOBYQA: unconstrained optimization by quadratic approximation
- Least Frobenius norm updating of quadratic models that satisfy interpolation conditions
- Nonlinear robust optimization via sequential convex bilevel programming
- An approximation technique for robust nonlinear optimization
- A numerical approach for shape optimization of fluid flow domains
- A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
- Robust Convex Optimization
- Minimizing a Quadratic Over a Sphere
- A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization
- A polynomial chaos meta‐model for non‐linear stochastic magnet variations
- Extended Brauer model for ferromagnetic materials: analysis and computation
- Newton Methods for Nonlinear Problems
- Robust Optimization for Unconstrained Simulation-Based Problems
- Theory and Applications of Robust Optimization
- Computing a Trust Region Step
- Complementarity constraints as nonlinear equations: Theory and numerical experience
- Optimization with PDE Constraints
- Algorithm 873
- Lectures on Stochastic Programming
- The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
- Optimization and nonsmooth analysis
- Newton’s Method with a Model Trust Region Modification
- On the Extension of Constrained Optimization Algorithms from Differentiable to Nondifferentiable Problems
- A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results
- Generalized Gradients and Applications
- Introduction to Stochastic Programming
- Algorithm 799: revolve
- Trust Region Methods
- Solving mathematical programs with complementarity constraints as nonlinear programs
- The trust region subproblem and semidefinite programming*
- Optimal Control of Stochastic Partial Differential Equations
- Solving the Trust-Region Subproblem using the Lanczos Method
- Introduction to Shape Optimization
- Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
- A BFGS-SQP method for nonsmooth, nonconvex, constrained optimization and its evaluation using relative minimization profiles
- A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
- Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations
- Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk