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math.OC2021
Optimal Control of the Kirchhoff Equation
Masoumeh Hashemi, Roland Herzog, Thomas M. Surowiec
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed…
math.OC2021★ 2 cited
Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty
Werner Römisch, Thomas M. Surowiec
Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence ra…