Optimal control of a quasi-variational sweeping process

The paper addresses the study of a class of evolutionary quasi-variational inequalities arising in formation and growth models of granular and cohesionless materials. Such models and their mathematical descriptions are highly challenging and require powerful tools for their analysis and implementation. We formulated a space-time continuous optimal control problem for a basic model of this type, developed several regularization and approximation procedures, and established the existence of optimal solutions for the time-continuous and space-discrete problem. Viewing a version of this problem as a controlled quasi-variational sweeping process leads us to derive necessary optimality conditions for the fully discrete problem by using the advanced machinery of variational analysis and generalized differentiation.