Renato D.C. Monteiro – Page 4 – Optimization Online

Convex and Nonsmooth Optimization

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 … Read more

An accelerated HPE-type algorithm for a class of composite convex-concave saddle-point problems

Published: 2014/04/29

Yunlong He

Convex Optimization, Generalized Convexity/Monoticity, Nonsmooth Optimization accelerated method, complexity, composite convex optimization, hybrid proximal extragradient, inexact proximal point method, monotone inclusion problem, saddle point problem, smoothing

This article proposes a new algorithm for solving a class of composite convex-concave saddle-point 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 … Read more

An inexact block-decomposition method for extra large-scale conic semidefinite programming

Published: 2013/12/11, Updated: 2014/02/01

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software and Modeling Systems block-decomposition, complexity, conic optimization, conjugate gradient method, extragradient, large-scale optimization, proximal, semidefinite programming

In this paper, we present an inexact block-decomposition (BD) first-order method for solving standard form conic semidefinite programming (SDP) which avoids computations of exact projections onto the manifold defined by the affine constraints and, as a result, is able to handle extra large SDP instances. The method is based on a two-block reformulation of the … Read more

Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems

Published: 2013/10/30, Updated: 2015/07/19

Yunlong He

Convex Optimization, Generalized Convexity/Monoticity, Nonsmooth Optimization block-decomposition, complexity, hybrid proximal extragradient, monotone variational inequality, nash equilibrium, nesterov's method, saddle point problem

This article considers the two-player composite Nash equilibrium (CNE) problem with a separable non-smooth part, which is known to include the composite saddle-point (CSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient (BD-HPE) framework. The framework consists of a … Read more

A hybrid proximal extragradient self-concordant primal barrier method for monotone variational inequalities

Published: 2013/08/09, Updated: 2013/08/23

Complementarity and Variational Inequalities hybrid extragradient proximal point method, monotone variational inquality

Mauricio Romero

In this paper we present a primal interior-point hybrid proximal extragradient (HPE) method for solving a monotone variational inequality over a closed convex set endowed with a self-concordant barrier and whose underlying map has Lipschitz continuous derivative. In contrast to the method of “R. D. C. Monteiro and B. F. Svaiter, Iteration-Complexity of a Newton … Read more

An adaptive accelerated first-order method for convex optimization

Published: 2012/08/03, Updated: 2014/05/28

Convex Optimization, Nonsmooth Optimization accelerated gradient methods, complexity, conic optimization, convex optimization, quadratic programming

This paper presents a new accelerated variant of Nesterov’s method for solving composite convex optimization problems in which certain acceleration parameters are adaptively (and aggressively) chosen so as to substantially improve its practical performance compared to existing accelerated variants while at the same time preserve the optimal iteration-complexity shared by these methods. Computational results are … Read more

A first-order block-decomposition method for solving two-easy-block structured semidefinite programs

Published: 2012/07/28, Updated: 2013/10/14

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Optimization Software Benchmark block-decomposition, complexity, conic optimization, convex optimization, extragradient, proximal, semidefinite programming

In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for … Read more

Implementation of a block-decomposition algorithm for solving large-scale conic semidefinite programming problems

Published: 2011/05/13, Updated: 2013/09/12

Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming block-decomposition, complexity, conic optimization, convex optimization, extragradient, proximal, semidefinite programming

In this paper, we consider block-decomposition first-order methods for solving large-scale conic semidefinite programming problems. Several ingredients are introduced to speed-up the method in its pure form such as: an aggressive choice of stepsize for performing the extragradient step; use of scaled inner products in the primal and dual spaces; dynamic update of the scaled … Read more

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

Published: 2011/05/11, Updated: 2012/05/26