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math.OC2025
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…
math.OC2025
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,+\…
math.OC2025
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.…