208 citations · 557 across the 57 of their papers we have counts for
73 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…
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 class of monotone operator inclusion problems in Hilbert spaces. It is based on a reduced inclusion model with two oper…
Lower Bounds on the Haraux Function
Patrick L. Combettes, Julien N. Mayrand
The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in $[0,+\…
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.…
Variational Analysis of Proximal Compositions and Integral Proximal Mixtures
Patrick L. Combettes, Diego J. Cornejo
This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal…
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…