A Semismooth Newton Method for Regularized Lq-quasinorm Sparse Optimal Control Problems

Abstract

A semismooth Newton method (refered as DC–SSN) is proposed for the numerical solution of a class of nonconvex optimal control problems governed by linear elliptic partial differential equations. The nonconvex term in the cost functional arises from a Huber-type local regularization of the Lq-quasinorm (q ∈ (0, 1)), therefore it promotes sparsity on the solution. The DC–SSN method solves the optimality system of the regularized problem resulting from the application of difference-of-convex functions programming tools.