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Advanced seminar AG Mathematical Modeling
Monday, November 25, 2024 at 5 p.m. in B7 - 210
Talk by Pierre Marie Ngougoue Ngougoue (Clausthal) on "Random elliptic quasi-variational inequalities and risk-averse optimal control".
Title:
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 regularization of the obstacle problem yielding a well-defined regularised control problem. This regularization 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 regularized, smoothed problem and, through a limiting analysis with respect to the regularization 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.