In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval (0, 2) instead of interval (0, (1 + √ 5)/2). As usual, our analysis is established by interpreting this ADMM variant as an instance...

This paper presents and studies the iteration-complexity of two new inexact variants of Rockafellar’s proximal method of multipliers (PMM) for solving convex programming (CP) problems with a finite number of functional inequality constraints. In contrast to the first variant which solves convex quadratic programming (QP) subproblems at every iteration, the second one solves convex constrained q...

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optimal O(1/k) rate of convergence. Compared to the optimal non-SP algorithms, our...

This article proposes a new algorithm for solving a class of composite convex-concave saddlepoint problems. The new algorithm is a special instance of the hybrid proximal extragradient framework in which a Nesterov’s accelerated variant is used to approximately solve the prox subproblems. One of the advantages of the new method is that it works for any constant choice of proximal stepsize. More...

In this paper, we present a new hybrid extragradient algorithm for finding common element of the fixed point problem demicontractive mapping and split equilibrium pseudomonotone Lipschitz-type continuous bifunction. By using technique choosing step size proposed method, our algorithms do not need any prior information operator norm. fact, propose an inertial type in order to accelerate its conv...

In this paper, we consider both a variant of Tseng’s modified forward-backward splitting method and an extension of Korpelevich’s method for solving hemivariational inequalities with Lipschitz continuous operators. By showing that these methods are special cases of the hybrid proximal extragradient method introduced by Solodov and Svaiter, we derive iteration-complexity bounds for them to obtai...

Abstract In a real Banach space, let the VI indicate variational inclusion for two accretive operators and CFPP denote common fixed point problem of countably many nonexpansive mappings. this article, we introduce generalized extragradient implicit method solving general system inequalities (GSVI) with constraints. Strong convergence suggested to solution GSVI constraints under some suitable as...

This paper describes an accelerated HPE-type method based on general Bregman distances for solving monotone saddle-point (SP) problems. The algorithm is a special instance of a non-Euclidean hybrid proximal extragradient framework introduced by Svaiter and Solodov [28] where the prox sub-inclusions are solved using an accelerated gradient method. It generalizes the accelerated HPE algorithm pre...

We present a method to simultaneously learn a mixture of mappings and large margin hyperplane classifier. This method learns useful mappings of the training data to improve classification accuracy. We first present a simple iterative algorithm that finds a greedy local solution and then derive a semidefinite relaxation to find an approximate global solution. This relaxation leads to the matrix ...