arXiv subjects

Majela Pentón Machado

Publications and source records attributed to Majela Pentón Machado.

4 recordsLinked to original sources

arXiv2020

Random iterations of paracontraction maps and applications to feasibility problems

In this paper, we consider the problem of finding an almost surely common fixed point of a family of paracontraction maps indexed on a probability space, which we refer to as the stochastic feasibility problem. We show that a random iteration of paracontraction maps driven by an ergodic stationary sequence converges, with probability one, to a solution of the stochastic feasibility problem, provided a solution exists. As applications, we obtain non-white noise randomized algorithms to solve the stochastic convex feasibility problem and the problem of finding an almost surely common zero of a collection of maximal monotone operators.

math.DS↗

arXiv2019

Inexact proximal $ε$-subgradient methods for composite convex optimization problems

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator and approximate subgradients of the functions (namely: the $ε$-subgradients). The methods use different error criteria for approximating the proximal operators. We provide an analysis of the convergence and rate of convergence properties of these methods, considering various stepsize rules, including both, diminishing and constant stepsizes. For the case where one of the functions is smooth, we propose an inexact accelerated version of the proximal gradient method, and prove that the optimal convergence rate for the function values can be achieved.

math.OC↗

arXiv2018

On the complexity of the projective splitting and Spingarn's methods for the sum of two maximal monotone operators

In this work we study the pointwise and ergodic iteration-complexity of a family of projective splitting methods proposed by Eckstein and Svaiter, for finding a zero of the sum of two maximal monotone operators. As a consequence of the complexity analysis of the projective splitting methods, we obtain complexity bounds for the two-operator case of Spingarn's partial inverse method. We also present inexact variants of two specific instances of this family of algorithms, and derive corresponding convergence rate results.

math.OC↗

arXiv2017

Projective method of multipliers for linearly constrained convex minimization

We present a method for solving linearly constrained convex optimization problems, which is based on the application of known algorithms for finding zeros of the sum of two monotone operators (presented by Eckstein and Svaiter) to the dual problem. We establish convergence rates for the new method, and we present applications to TV denoising and compressed sensing problems.

math.OC↗