Optimal control of a quasi-variational sweeping process
Year: 2025
Type: article
Abstract: 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.
DOI: 10.3934/mcrf.2025010
Institutions: George Mason University, University of Michigan
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: National Science Foundation
Awards: Algorithms and Numerical Methods for Optimization with Partial Differential Equation Constraints, Optimization Problems with Quasi-Equilibrium Constraints: Control, Identification, and Design, G4410295239, Variational Analysis: Theory, Algorithms, and Applications, Advanced Research on Second-Order Variational Analysis with New Applications to Optimization, Control, and Practical Modeling, Collaborative Research: Multilevel Methods for Optimal Control of Partial Differential Equations and Optimization-Based Domain Decomposition
OpenAlex ID: W4407601939