An algorithm using Moreau-Yosida regularization for minimization of a nondifferentiable convex function

Properties of the Moreau-Yosida regularization of a piecewise C2 convex function

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 ...

Lagrangian-Dual Functions and Moreau--Yosida Regularization

In this paper, we consider the Lagrangian dual problem of a class of convex optimization problems. We first discuss the semismoothness of the Lagrangian-dual function φ. This property is then used to investigate the second-order properties of the Moreau-Yosida regularization η of the function φ, e.g., the semismoothness of the gradient g of the regularized function η. We show that φ and g are p...

Moreau-Yosida Regularization for Grouped Tree Structure Learning

We consider the tree structured group Lasso where the structure over the features can be represented as a tree with leaf nodes as features and internal nodes as clusters of the features. The structured regularization with a pre-defined tree structure is based on a group-Lasso penalty, where one group is defined for each node in the tree. Such a regularization can help uncover the structured spa...

On Se ond-order Properties of the Moreau-Yosida Regularization for Constrained Nonsmooth Convex Programs

On Second-order Properties of the Moreau-Yosida Regularization for Constrained Nonsmooth Convex Programs

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C2 convex objectives with smooth convex inequality constraints. By using the Moreau-Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau-Yosida regularization η. By introdu...