Strengthened splitting methods for computing resolvents
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 …
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
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 …
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
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 …
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
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 …
to two nonorthogonal linear subspaces of a real Euclidean space. Assuming that both of the …
Coordinate-update algorithms can efficiently detect infeasible optimization problems
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 …
their low per-iteration cost and scalability, but their behavior on infeasible or misspecified …
Comparing averaged relaxed cutters and projection methods: theory and examples
We focus on the convergence analysis of averaged relaxations of cutters, specifically for
variants that—depending upon how parameters are chosen—resemble alternating …
variants that—depending upon how parameters are chosen—resemble alternating …
Error bounds for the method of simultaneous projections with infinitely many subspaces
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 …
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 …
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 …
los problemas de optimización aumenten progresivamente en tamaño y complejidad. Una …
On the convergence rate improvement of a splitting method for finding the resolvent of the sum of maximal monotone operators
S Matsushita - ar** the splitting method which is used to solve the
problem of finding the resolvent of the sum of maximal monotone operators in Hilbert …
problem of finding the resolvent of the sum of maximal monotone operators in Hilbert …