Oberseminar AG Mathematische Modellierung

Montag, den 25.11.2024 um 17.00 Uhr in B7 - 210

Vortrag von Pierre Marie Ngougoue Ngougoue (Clausthal) zum Thema „Random elliptic quasi-variational inequalities and risk-averse optimal control“.

Titel:  

We investigate a risk-averse optimal control problem governed by an elliptic quasi-variational inequality (QVI) subject to random inputs. By extending existing methods in stochastic mathematical programs with equilibrium constraints (SMPECs), we introduce a penalty-based regularisation of the obstacle problem yielding a well-defined regularised control problem. This regularisation maintains consistency with the primal control problem and provides a robust framework for further analysis. Building on this, we derive the stationarity conditions for the regularised, smoothed problem and, through a limiting analysis with respect to the regularisation parameter, establish C-stationarity conditions for the primal control problem. The introduction of uncertainty quantification and the solution-dependent obstacle map – unique to QVIs – give rise to significant challenges, particularly in terms of measurability and solution existence. While the framework is primarily theoretical, its practical relevance is demonstrated through an application to thermoforming processes with uncertain material properties.