TITLE:
Proximal Methods for Elliptic Optimal Control Problems with Sparsity Cost Functional
AUTHORS:
Andreas Schindele, Alfio Borzì
KEYWORDS:
Optimal Control, Elliptic PDE, Nonsmooth Optimization, Proximal Method, Semismooth Newton Method
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.9,
May
30,
2016
ABSTRACT: First-order proximal methods that solve
linear and bilinear elliptic optimal control problems with a sparsity cost
functional are discussed. In particular, fast convergence of these methods is
proved. For benchmarking purposes, inexact proximal schemes are compared to an
inexact semismooth Newton method. Results of numerical experiments are presented
to demonstrate the computational effectiveness of proximal schemes applied to
infinite-dimensional elliptic optimal control problems and to validate the
theoretical estimates.