Optimality conditions for locally Lipschitz optimization with \(l_0\)-regularization (Q1996752)

In this paper the authors consider the locally Lipschitz optimization problem (LLOP) with \(l_0\)-regularization in a finite dimensional space. The authors introduced and analyzed two classes of stationary points for this problem: subdifferential-stationary point (S-stationary point) and proximal-stationary point (P-stationary point). The first-order sufficient and necessary optimality conditions for the LLOP under some suitable conditions are presented. Two examples illustrate the validity of the considered optimality conditions.