— In this paper, we deal with sweeping processes on (possibly infinitedimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of th...

Prox-regularity of a set (Poliquin-Rockafellar-Thibault, 2000), or its global version, proximal smoothness (Clarke-Stern-Wolenski, 1995) plays an important role in variational analysis, not only because it is associated with some fundamental properties as the local continuous differentiability of the function dist (C; ·), or the local uniqueness of the projection mapping, but also because in th...

<p style='text-indent:20px;'>The aim of this paper is to study a wide class non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i. e., functions not necessarily bounded variation admitting one-sided limits at every point. Assuming that the time-dependent uniformly prox-regular has non-empty interior, we prove exist...

We consider minimization of functions that are compositions of prox-regular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a regularization term, investigating the properties of local solutions of this subproblem and showing that the...

In this paper, we provide in a general Hilbert space new characterizations of uniform prox-regularity involving outside but sufficiently close points considered sets. We show that the complement prox-regular set is nothing union closed balls with common radius. derive from given equivalent to semiconvexity property its distance function. Various estimates metric projection mapping are also esta...

This paper mainly studies the quadratic growth and strong metric subregularity of subdifferential a function that can be represented as sum twice differentiable in extended sense subdifferentially continuous, prox-regular, epi-differentiable function. For such function, which is not necessarily it shown growth, at local minimizer, positive definiteness subgradient graphical derivative stationar...