arXiv subjects

Diego J. Cornejo

Publications and source records attributed to Diego J. Cornejo.

4 recordsLinked to original sources

arXiv2026

Proximal Comixture Minimization Models for Image Recovery and Data Analysis

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 the aggregate models a desired property of the ideal solution arising from the \emph{a priori} knowledge and the observed data. We propose an alternative minimization model based on proximal comixtures, an operation which combines functions and linear operators in such a way that the proximity operator of the resulting function is computable explicitly in terms of the individual proximity and linear operators. The mathematical properties of this operation are analyzed and comparisons between proximal comixtures and standard composite averages are made. Numerical illustrations of the benefits of minimization models based on proximal comixtures are provided in the context of image recovery and machine learning applications.

math.OC↗

arXiv2026

Resolvent Compositions for Positive Linear Operators

Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the resolvent compositions when the monotone operator is a positive linear operator. We establish several new properties, including Löwner partial order relations, concavity, and asymptotic behavior. In addition, we show that the resolvent composition operations are nonexpansive with respect to the Thompson metric. We also introduce a new form of geometric interpolation and explore its connections to resolvent compositions. Finally, we study two nonlinear equations based on resolvent compositions.

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arXiv2025

Parametrized Families of Resolvent Compositions

This paper presents an in-depth analysis of a parametrized version of the resolvent composition, an operation that combines a set-valued operator and a linear operator. We provide new properties and examples, and show that resolvent compositions can be interpreted as parallel compositions of perturbed operators. Additionally, we establish new monotonicity results, even in cases when the initial operator is not monotone. Finally, we derive asymptotic results regarding operator convergence, specifically focusing on graph-convergence and the $ρ$-Hausdorff distance.

math.OC↗

arXiv2025

Variational Analysis of Proximal Compositions and Integral Proximal Mixtures

This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the integral proximal mixture of arbitrary families of functions and linear operators. We study in particular convexity, Legendre conjugacy, differentiability, Moreau envelopes, coercivity, minimizers, recession functions, and perspective functions of these constructs, as well as their asymptotic behavior as the parameter varies. The special case of the proximal expectation of a family of functions is also discussed.

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