6 papers
Almost Supermartingale Extensions of Olivier's Theorem
Patrick L. Combettes, Javier I. Madariaga
Olivier's 1827 theorem provides a rate of convergence to zero of the general term of a decreasing summable sequence of positive reals. We derive stochastic extensions of this resul…
Convergence of the Iterates of the Stochastic Proximal Gradient Method
Javier I. Madariaga
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without r…
An Abstract Stochastic Haugazeau Method for Best Approximation
Javier I. Madariaga
The Haugazeau method was originally designed to compute the best approximation from an intersection of closed convex sets in Hilbert spaces using the projection operators onto the…
A Geometric Framework for Stochastic Iterations
Patrick L. Combettes, Javier I. Madariaga
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces.…
Asymptotic Analysis of an Abstract Stochastic Scheme for Solving Monotone Inclusions
Patrick L. Combettes, Javier I. Madariaga
We propose an abstract stochastic scheme for solving a broad range of monotone operator inclusion problems in Hilbert spaces. This framework allows for the introduction of stochast…
Almost-Surely Convergent Randomly Activated Monotone Operator Splitting Methods
Patrick L. Combettes, Javier I. Madariaga
We propose stochastic splitting algorithms for solving large-scale composite inclusion problems involving monotone and linear operators. They activate at each iteration blocks of r…