Abstract In this paper our interest is in investigating properties and numerical solutions of Proximal Split feasibility Problems. First, we consider the problem of finding a point which minimizes a convex function f such that its image under a bounded linear operator A minimizes another convex function g. Based on an idea introduced in [9], we propose a split proximal algorithm with a way of s...

In this articlewe discuss the differential inclusion known as state dependent sweeping process for a class of prox-regular non-convex sets.We associate with any state dependent sweeping process with such sets an unconstraint differential inclusion whose any solution is a solution of the state sweeping process too. We prove a theorem on the existence of a global solution of nonconvex state depen...

The human neurofilament (H) promoter contains multiple binding sites for nuclear proteins including a Proximal (Prox) site centered around the sequence GGTTGGACC and an adjacent pyrimidine (Pyr) tract site centered around the sequence CCCTCCTCCCC. Surprisingly binding to a probe containing the Prox/Pyr region of the NF(H) promoter was competed in gel shifts by an oligonucleotide containing only...

In this paper, some systems of quasi-variational inequality problems are considered on a class of nonconvex sets, as uniformly prox-regular sets. Some sufficient conditions for the existence solution of the considered problems are provided. Also, some interesting remarks are discussed. The results which are presented in this paper are more general, and may be viewed as an extension, improvement...

Consensus optimization has received considerable attention in recent years. A number of decentralized algorithms have been proposed for convex consensus optimization. However, on consensus optimization with nonconvex objective functions, our understanding to the behavior of these algorithms is limited. When we lose convexity, we cannot hope for obtaining globally optimal solutions (though we st...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

We study an optimal control problem consisting in minimizing the L∞ norm of a Borel measurable cost function, finite time, and over all trajectories associated with controlled dynamics which is reflected compact prox-regular set. The first part paper provides viscosity characterization value function for uniformly continuous costs. second concerned linear programming formulations ensued by-prod...