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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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