The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by a uniformly prox-regular set. After obtaining well-posedness results, we propose a numerical scheme based on a predictioncorrection algorithm and we prove its convergence. Finally we apply these results to a problem coming from modelling of crowd ...

Prox 1 is a vertebrate homeobox gene which is homologous to the Drosophila transcription factor, prospero. We have isolated a prox 1 cDNA from zebrafish, which encodes a protein that has 82%, 84% and 83% amino acid identity with chicken, mouse and human Prox 1, respectively. Antibodies raised against human Prox 1 cross-react with zebrafish Prox 1 and are used here to determine the expression pa...

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a ra...

It is known that the subdifferential of a lower semicontinuous convex function f over a Banach space X determines this function up to an additive constant in the sense that another function of the same type g whose subdifferential coincides with that of f at every point is equal to f plus a constant, i.e., g = f + c for some real constant c. Recently, Thibault and Zagrodny introduced a large cl...

Abstract. We propose a prox-type method with efficiency estimate O(2−1) for approximating saddle points of convex-concave C1,1 functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization and computing Lovasz capacity number of a graph and are illustrated by numerical experiments with large-s...

In this short survey, I revisit the role of the proximal point method in large scale optimization. I focus on three recent examples: a proximally guided subgradient method for weakly convex stochastic approximation, the prox-linear algorithm for minimizing compositions of convex functions and smooth maps, and Catalyst generic acceleration for regularized Empirical Risk Minimization.

and Applied Analysis 3 the uniform r-prox-regularity C is equivalent to the convexity of C. Moreover, it is clear that the class of uniformly prox-regular sets is sufficiently large to include the class p-convex sets, C1,1 submanifolds possibly with boundary of H, the images under a C1,1 diffeomorphism of convex sets, and many other nonconvex sets; see 6, 8 . Now, let us state the following fac...