82 citations · 312 across the 12 of their papers we have counts for
13 papers
Strengthened Splitting Methods for Computing Resolvents
Francisco J. Aragón Artacho, Rubén Campoy, Matthew K. Tam
In this work, we develop a systematic framework for computing the resolvent of the sum of two or more monotone operators which only activates each operator in the sum individually.…
The Douglas-Rachford Algorithm for Convex and Nonconvex Feasibility Problems
Francisco J. Aragón Artacho, Rubén Campoy, Matthew K. Tam
The Douglas-Rachford method, a projection algorithm designed to solve continuous optimization problems, forms the basis of a useful heuristic for solving combinatorial optimization…
Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm
F. J. Aragón Artacho, R. Campoy
The averaged alternating modified reflections algorithm is a projection method for finding the closest point in the intersection of closed convex sets to a given point in a Hilbert…
The Cyclic Douglas-Rachford Algorithm with r-sets-Douglas-Rachford Operators
Francisco J. Aragón Artacho, Yair Censor, Aviv Gibali
The Douglas-Rachford (DR) algorithm is an iterative procedure that uses sequential reflections onto convex sets and which has become popular for convex feasibility problems. In thi…
Optimal rates of linear convergence of the averaged alternating modified reflections method for two subspaces
Francisco J. Aragón Artacho, Rubén Campoy
The averaged alternating modified reflections (AAMR) method is a projection algorithm for finding the closest point in the intersection of convex sets to any arbitrary point in a H…
A feasibility approach for constructing combinatorial designs of circulant type
Francisco J. Aragón Artacho, Rubén Campoy, Ilias Kotsireas +1
In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem…
Solving graph coloring problems with the Douglas-Rachford algorithm
Francisco J. Aragón Artacho, Rubén Campoy
We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color…
A new projection method for finding the closest point in the intersection of convex sets
Francisco J. Aragón Artacho, Rubén Campoy
In this paper we present a new iterative projection method for finding the closest point in the intersection of convex sets to any arbitrary point in a Hilbert space. This method,…
Accelerating the DC algorithm for smooth functions
Francisco J. Aragón Artacho, Ronan M. T. Fleming, Phan T. Vuong
We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point…
Global Behavior of the Douglas-Rachford Method for a Nonconvex Feasibility Problem
Francisco J. Aragón Artacho, Jonathan M. Borwein, Matthew K. Tam
In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For man…
Recent Results on Douglas-Rachford Methods for Combinatorial Optimization Problems
Francisco J. Aragón Artacho, Jonathan M. Borwein, Matthew K. Tam
We discuss recent positive experiences applying convex feasibility algorithms of Douglas--Rachford type to highly combinatorial and far from convex problems.
Applications of Convex Analysis within Mathematics
Francisco J. Aragón Artacho, Jonathan M. Borwein, Victoria Martín-Márquez +1
In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various de…
Global convergence of a non-convex Douglas-Rachford iteration
Francisco J. Aragón Artacho, Jonathan M. Borwein
We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on th…