Reduced basis methods- an application to variational discretization of\n parametrized elliptic optimal control problems

2018/08/16 by Ahmad Ahmad Ali, Ali, Ahmad Ahmad, Michael Hinze +1 · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1808.05687

openalex publication_date 2018/08/16 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

We consider a class of parameter-dependent optimal control problems of\nelliptic PDEs with constraints of general type on the control variable.\nApplying the concept of variational discretization, [4], together with\ntechniques from the Reduced basis method, we construct a reduced basis\nsurrogate model for the control problem. We establish estimators for the greedy\nsampling procedure which only involve the residuals of the state and the\nadjoint equation, but not of the gradient equation of the optimality system.\nThe estimators are sharp up to a constant, i.e. they are equivalent to the\napproximation erros in control, state, and adjoint state. Numerical experiments\nshow the performance of our approach.\n

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