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Properties of the Moreau-Yosida regularization of a piecewise \(C^2\) convex function. (English) Zbl 0971.90082
Summary: In this paper we discuss second-order properties of the Moreau-Yosida regularization \(F\) of a piecewise twice continuously differentiable convex function \(f\). We introduce a new constraint qualification in order to prove that the gradient of \(F\) is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness of the generalized Jacobians of the gradient of \(F\).

MSC:
90C30 Nonlinear programming
90C25 Convex programming
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