Strengthened splitting methods for computing resolvents

FJ Aragón Artacho, R Campoy, MK Tam - Computational Optimization and …, 2021 - Springer
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 …

Polynomial estimates for the method of cyclic projections in Hilbert spaces

S Reich, R Zalas - Numerical Algorithms, 2023 - Springer
We study the method of cyclic projections when applied to closed and linear subspaces M i,
i= 1,…, m, of a real Hilbert space H. We show that the average distance to individual sets …

Computing the resolvent of the sum of maximally monotone operators with the averaged alternating modified reflections algorithm

FJ Aragón Artacho, R Campoy - Journal of Optimization Theory and …, 2019 - Springer
The averaged alternating modified reflections algorithm is a projection method for finding the
closest point in the intersection of closed and convex sets to a given point in a Hilbert space …

Comparing the methods of alternating and simultaneous projections for two subspaces

S Reich, R Zalas - Linear Algebra and its Applications, 2024 - Elsevier
We study the well-known methods of alternating and simultaneous projections when applied
to two nonorthogonal linear subspaces of a real Euclidean space. Assuming that both of the …

Coordinate-update algorithms can efficiently detect infeasible optimization problems

J Paeng, J Park, EK Ryu - Journal of Mathematical Analysis and …, 2025 - Elsevier
Coordinate update/descent algorithms are widely used in large-scale optimization due to
their low per-iteration cost and scalability, but their behavior on infeasible or misspecified …

Comparing averaged relaxed cutters and projection methods: theory and examples

RD Millán, SB Lindstrom, V Roshchina - Jonathan M. Borwein …, 2017 - Springer
We focus on the convergence analysis of averaged relaxations of cutters, specifically for
variants that—depending upon how parameters are chosen—resemble alternating …

Error bounds for the method of simultaneous projections with infinitely many subspaces

S Reich, R Zalas - Journal of Approximation Theory, 2021 - Elsevier
We investigate the properties of the simultaneous projection method as applied to countably
infinitely many closed and linear subspaces of a real Hilbert space. We establish the optimal …

[PDF][PDF] Proximal point algorithms, dynamical systems, and associated operators: modern perspectives from experimental mathematics

SB Lindstrom - University of Newcastle, 2018 - nova.newcastle.edu.au
Discrete dynamical systems are ubiquitous in many mathematical disciplines. Celebrated
methods as old as the Hellenic period include Euclid's algorithm on Z2 and continued …

Splitting algorithms for structured optimization: theory and applications

D Torregrosa Belén - Proyecto de investigación:, 2024 - digitum.um.es
Los avances actuales en tecnología y el incremento de información disponible hacen que
los problemas de optimización aumenten progresivamente en tamaño y complejidad. Una …