This paper deals with split equilibrium problems in Banach spaces. The presented algorithm is based on the hybrid and proximal point has been used for finding solution of problems. Under some standard assumptions bifunctions, it proven that generated sequences by scheme are strongly convergent. Finally, efficiency proposed method demonstrated through examples. Also, comparative results verify m...

High-Dimensional Gaussian Sampling: A Review and a Unifying Approach Based on Stochastic Proximal Point Algorithm

We propose a modification of the classical extragradient and proximal point algorithms for finding a zero of a maximal monotone operator in a Hilbert space. At each iteration of the method, an approximate extragradient-type step is performed using information obtained from an approximate solution of a proximal point subproblem. The algorithm is of a hybrid type, as it combines steps of the extr...

In this work, we propose a proximal algorithm for unconstrained optimization on the cone of symmetric semidefinite positive matrices. It appears to be the first in the proximal class on the set of methods that convert a Symmetric Definite Positive Optimization in Nonlinear Optimization. It replaces the main iteration of the conceptual proximal point algorithm by a sequence of nonlinear programm...

The proximal method is a standard regularization approach in optimization. Practical implementations of this algorithm require (i) an algorithm to compute the proximal point, (ii) a rule to stop this algorithm, (iii) an update formula for the proximal parameter. In this work we focus on (ii), when smoothness is present – so that Newton-like methods can be used for (i): we aim at giving adequate...

We provide a new perspective to understand proximal gradient algorithms. We show that both proximal gradient algorithm (PGA) and Bregman proximal gradient algorithm (BPGA) can be viewed as generalized proximal point algorithm (GPPA), based on which more accurate convergence rates of PGA and BPGA are obtained directly. Furthermore, based on GPPA framework, we incorporate the back-tracking line s...

This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum locally accessible convex functions subject feasible set constraint coupled inequality constraints whose information is only partially each agent. For this problem, proximal-based algorithm, called proximal primal-dual (DPPD) proposed based ...

The proximal point algorithm (PPA) is classical and popular in the community of Optimization. In practice, inexact PPAs which solves the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact PPA with a new inexact criterion for solving convex minimization, and show that the iteration-complexity of this...