Risk-averse optimal control of random elliptic variational inequalities

Autor:	Alphonse, Amal, Geiersbach, Caroline, Hintermüller, Michael, Surowiec, Thomas M.
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the stationary points with respect to the penalisation parameter, we obtain two forms of stationarity conditions. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to new challenges unique to the stochastic setting. We also propose a path-following stochastic approximation algorithm using variance reduction techniques and demonstrate the algorithm on a modified benchmark problem. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2210.03425 Zobrazit plný text záznamu View this record from Arxiv