Work

Homotopy trust-region method for phase-field approximations in perimeter-regularized binary optimal control

Year: 2024

Type: article

Abstract: We consider optimal control problems that have binary-valued control input functions and a perimeter regularization. We develop and analyze a trust-region algorithm that solves a sequence of subproblems in which the regularization term and the binarity constraint are relaxed by a non-convex energy functional. We show how the parameter that controls the distinctiveness of the resulting phase field can be coupled to the trust-region radius updates and be driven to zero over the course of the iterations in order to obtain convergence to points that satisfy a first-order optimality condition of the limit problem under suitable regularity assumptions. Finally, we highlight and discuss the assumptions and restrictions of our approach and provide the first computational results for a motivating application in the field of control of acoustic waves in dissipative media.

Source: ESAIM Control Optimisation and Calculus of Variations

DOI: 10.1051/cocv/2024075

Authors: Paul Manns, Vanja Nikolić

Institutions: TU Dortmund University, Radboud University Nijmegen

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid:

Funders: Deutsche Forschungsgemeinschaft, Technische Universität Dortmund