Proximal schemes for parabolic optimal control problems with sparsity promoting cost functionals

Abstract

ABSTRACTFast first-order proximal methods that solve linear and bilinear parabolic optimal control problems with a sparsity cost functional are discussed. Weak convergence of these methods is proved and, for benchmarking purposes, the proposed inexact proximal schemes are compared to an inexact semi-smooth Newton method. Results of numerical experiments are presented to demonstrate the computational effectiveness of proximal schemes and to validate the theoretical estimates.