Complexity Analysis of stochastic gradient methods for PDE-constrained optimal Control Problems with uncertain parameters

DOI10.1051/m2an/2021025zbMath1492.35394OpenAlexW3164869052WikidataQ114105433 ScholiaQ114105433MaRDI QIDQ5074382

Matthieu Martin, Fabio Nobile, Sebastian Krumscheid

Publication date: 9 May 2022

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2021025

zbMATH Keywords

Monte Carlostochastic approximationsample average approximationstochastic gradientPDE constrained optimizationoptimization under uncertaintyPDE with random coefficientsrisk-averse optimal control

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Smoothness and regularity of solutions to PDEs (35B65) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs in connection with control and optimization (35Q93) PDE constrained optimization (numerical aspects) (49M41)

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Uses Software

• FreeFem++

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