Work

Risk-averse optimal control of random elliptic variational inequalities

Year: 2025

Type: article

Abstract: 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.

Source: Springer Link (Chiba Institute of Technology)

DOI: 10.1051/cocv/2025045/pdf

Authors: Amal Alphonse, Caroline Geiersbach, Michael Hintermüller, Thomas M. Surowiec

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Universität Hamburg, Simula Research Laboratory

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: G188083318, G356062454