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

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

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 ...

Primal-Dual Extragradient Methods for Nonlinear Nonsmooth PDE-Constrained Optimization

We study the extension of the Chambolle–Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity of the corresponding primal-dual optimality conditions. We also show convergence for a Nesterov-type accelerated variant provided one part of the functional i...

Practical Aspects of the Moreau-Yosida Regularization: Theoretical Preliminaries

When computing the infimal convolution of a convex function f with the squared norm, the so-called Moreau–Yosida regularization of f is obtained. Among other things, this function has a Lipschitzian gradient. We investigate some more of its properties, relevant for optimization. The most important part of our study concerns second-order differentiability: existence of a secondorder development ...

A Modified Fletcher-Reeves-Type Method for Nonsmooth Convex Minimization

Conjugate gradient methods are efficient for smooth optimization problems, while there are rare conjugate gradient based methods for solving a possibly nondifferentiable convex minimization problem. In this paper by making full use of inherent properties of Moreau-Yosida regularization and descent property of modified conjugate gradient method we propose a modified Fletcher-Reeves-type method f...