Sum theorems for maximal monotone operators under weak compactness conditions

This note presents a summary of our most recent results concerning the maximal monotonicity of the sum of two maximal monotone operators defined in a locally convex space under the classical interiority qualification condition when one of their domains or ranges has a weak relative compactness property. Citation NA Article Download View Sum theorems for … Read more

An accelerated non-Euclidean hybrid proximal extragradient-type Algorithm for convex-concave saddle-point Problems

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 presented … Read more

An Accelerated Hybrid Proximal Extragradient Method for Convex Optimization and its Implications to Second-Order Methods

This paper presents an accelerated variant of the hybrid proximal extragradient (HPE) method for convex optimization, referred to as the accelerated HPE (A-HPE) method. Iteration-complexity results are established for the A-HPE method, as well as a special version of it, where a large stepsize condition is imposed. Two specific implementations of the A-HPE method are … Read more

Iteration-Complexity of a Newton Proximal Extragradient Method for Monotone Variational Inequalities and Inclusion Problems

In a recent paper by Monteiro and Svaiter, a hybrid proximal extragradient framework has been used to study the iteration-complexity of a first-order (or, in the context of optimization, second-order) method for solving monotone nonlinear equations. The purpose of this paper is to extend this analysis to study a prox-type first-order method for monotone smooth … Read more

On the complexity of the hybrid proximal extragradient method for the iterates and the ergodic mean

In this paper we analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter. One of the key points of our analysis is the use of new termination criteria based on the $\varepsilon$-enlargement of a maximal monotone operator. The advantage … Read more