In the setting adopted by Edmond and Thibault [Mathematical Programming 104 (2005), 347--373], we study a class of perturbed sweeping processes. Under suitable assumptions, obtain two solution existence theorems for processes with constraint sets being prox-regular sublevel sets. The results are applied to analyzing behavior some concrete mechanical processes, which appear first time in this pa...

In this paper, we introduce a stochastic projected subgradient method for weakly convex (i.e., uniformly prox-regular) nonsmooth, nonconvex functions—a wide class of functions which includes the additive and convex composite classes. At a high-level, the method is an inexact proximal point iteration in which the strongly convex proximal subproblems are quickly solved with a specialized stochast...

Abstract: We prove an existence and uniqueness result for the solutions to the Skorokhod problem on uniformly prox-regular sets through a deterministic approach. This result can be applied in order to investigate some regularity properties of the value function for differential games with reflection on the boundary.

The minimization of an objective function over a constraint set can often be simplified if the “active manifold” of the constraints set can be correctly identified. In this work we present a simple subproblem, which can be used inside of any (convergent) optimization algorithm, that will identify the active manifold of a “prox-regular partly smooth” constraint set in a finite number of iterations.

We study the well-posedness of a class of nonlocal-interaction equations on general domains Ω⊂Rd , including nonconvex ones. We show that under mild assumptions on the regularity of domains (uniform prox-regularity), for λ -geodesically convex interaction and external potentials, the nonlocal-interaction equations have unique weak measure solutions. Moreover, we show quantitative estimates on t...

A controlled sweeping process with prox-regular set, $$W^{1,2}$$ -controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions established local optimality conditions are derived via strong converging continuous approximations, whose state entirely resides the interior set. Consequently, subdifferentials smaller than standard ones now employed results.

In this paper we establish criteria for the stability of the proximal mapping Prox φ = (∂φ+∂f)−1 associated to the proper lower semicontinuous convex functions φ and f on a reflexive Banach space X.We prove that, under certain conditions, if the convex functions φn converge in the sense of Mosco to φ and if ξn converges to ξ, then Prox f φn(ξn) converges to Prox f φ(ξ). 1. Preliminaries Let X b...

The objective of this research consisted of developing the two following thermal food processing software: “F-CALC” is software developed to carry out thermal process calculations based on the wellknown Ball's formula method, and “OPT-PROx” is software for thermal food processing optimization based on variable retort temperature processing and global optimization technique. Time-temperature dat...