6 papers · 1 filter
Proximal Comixture Minimization Models for Image Recovery and Data Analysis
Patrick L. Combettes, Diego J. Cornejo
In minimization models for image recovery and data analysis problems, loss functions and linear operators are typically aggregated as an average of composite terms. Each term in th…
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…
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,+\…
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…
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…