Work

Variational analysis of proximal compositions and integral proximal mixtures

Year: 2025

Type: article

Abstract: 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.

Source: Evolution equations and control theory

DOI: 10.3934/eect.2025017

Authors: Patrick L. Combettes, Diego J. Cornejo

Institution: North Carolina State University

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: CIF: Small: Signal Recovery Beyond Minimization: A Monotone Inclusion Framework