An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization
From MaRDI portal
Publication:5081087
DOI10.1137/20M134664XzbMath1493.90120OpenAlexW4281552282WikidataQ114074189 ScholiaQ114074189MaRDI QIDQ5081087
Michael Ulbrich, Johannes Milz
Publication date: 1 June 2022
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m134664x
distributionally robust optimizationsmoothing methodssmoothing functionstrust-region problemPDE-constrained optimization under uncertainty
Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Approximation methods and heuristics in mathematical programming (90C59) Robustness in mathematical programming (90C17)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Algorithms with adaptive smoothing for finite minimax problems
- Moment inequalities for sums of random matrices and their applications in optimization
- A feasible direction method for the semidefinite program with box constraints
- Automated solution of differential equations by the finite element method. The FEniCS book
- Parametric sensitivity analysis of perturbed PDE optimal control problems with state and control constraints
- Smoothing technique and its applications in semidefinite optimization
- General robust-optimization formulation for nonlinear programming
- Application of the augmented Lagrangian-SQP method to optimal control problems for the stationary Burgers equation
- A certified model reduction approach for robust parameter optimization with PDE constraints
- Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces
- An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty
- Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty
- Optimization of PDEs with uncertain inputs
- Hidden conic quadratic representation of some nonconvex quadratic optimization problems
- An approximation technique for robust nonlinear optimization
- Twice Differentiable Spectral Functions
- A Trust-Region Algorithm with Adaptive Stochastic Collocation for PDE Optimization under Uncertainty
- Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs
- Weak lower semi-continuity of the optimal value function and applications to worst-case robust optimal control problems
- A Multilevel Stochastic Collocation Algorithm for Optimization of PDEs with Uncertain Coefficients
- Distributionally Robust Convex Optimization
- Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs
- Optimizations for quadrature representations of finite element tensors through automated code generation
- DOLFIN
- Risk Averse Shape Optimization
- Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
- Computational Optimization of Systems Governed by Partial Differential Equations
- Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization
- Computing a Trust Region Step
- Optimization with PDE Constraints
- Shape Optimization Under Uncertainty—A Stochastic Programming Perspective
- Smoothing Methods and Semismooth Methods for Nondifferentiable Operator Equations
- Distributionally Robust Stochastic Programming
- A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems
- Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations
- trlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem
- Minimax analysis of stochastic problems
- Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints
- Weak Convergence of Measures
- Semiglobal optimal feedback stabilization of autonomous systems via deep neural network approximation
- PDE-Constrained Optimal Control Problems with Uncertain Parameters using SAGA
- Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters
- Accurately computing the log-sum-exp and softmax functions
- An Approximation Scheme for Distributionally Robust Nonlinear Optimization
- Epi-Regularization of Risk Measures
- Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets
- A Stochastic Gradient Method With Mesh Refinement for PDE-Constrained Optimization Under Uncertainty
- Stochastic Approximation for Optimization in Shape Spaces
- Taylor Approximation for Chance Constrained Optimization Problems Governed by Partial Differential Equations with High-Dimensional Random Parameters
- Inexact Objective Function Evaluations in a Trust-Region Algorithm for PDE-Constrained Optimization under Uncertainty
- An Inexact Bundle Algorithm for Nonconvex Nonsmooth Minimization in Hilbert Space
- Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method
- Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces
- Mesh Dependence in PDE-Constrained Optimisation
- Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations
- Ambiguity in portfolio selection
- Algorithm 839
- Unified form language
- Risk-Averse PDE-Constrained Optimization Using the Conditional Value-At-Risk
- A Quasi-Monte Carlo Method for Optimal Control Under Uncertainty
