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 L~q-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.
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