Calculus of Variations and Geometric Measure Theory

L. Portinale - U. Stefanelli

Penalization via global functionals of optimal-control problems for dissipative evolution

created by portinale on 22 Jun 2021


Published Paper

Inserted: 22 jun 2021
Last Updated: 22 jun 2021

Journal: Advances in Mathematical Sciences and Applications
Year: 2019

ArXiv: 1910.10050 PDF


We consider an optimal control problem for an abstract nonlinear dissipative evolution equation. The differential constraint is penalized by augmenting the target functional by a nonnegative global-in-time functional which is null-minimized in the evolution equation is satisfied. Different variational settings are presented, leading to the convergence of the penalization method for gradient flows, noncyclic and semimonotone flows, doubly nonlinear evolutions, and GENERIC systems.