Proximal mappings and Moreau envelopes of single-variable convex piecewise cubic functions and multivariable gauge functions
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Abstract (arXiv)
This work presents a collection of useful properties of the Moreau envelope for finite-dimensional, proper, lower semicontinuous, convex functions. In particular, gauge functions and piecewise cubic functions are investigated and their Moreau envelopes categorized. Characterizations of convex Moreau envelopes are established; topics include strict convexity, strong convexity and Lipschitz continuity.
Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Sep 2019.
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Citing papers per year: 2022: 1; 2023: 1; 2024: 1; 2025: 1.
4 papers.
- 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Casecited by 12
- 2022A Non-Asymptotic Moreau Envelope Theory for High-Dimensional Generalized Linear Modelscited by 11
- 2024On the Convergence of FedProx with Extrapolation and Inexact Proxcited by 3
- 2025The Ball-Proximal (="Broximal") Point Method: a New Algorithm, Convergence Theory, and Applicationscited by 3
- 2025The Ball-Proximal (="Broximal") Point Method: a New Algorithm, Convergence Theory, and Applications4 Feb 2025
- 2024On the Convergence of FedProx with Extrapolation and Inexact Prox2 Oct 2024
- 2023Kinetic Langevin MCMC Sampling Without Gradient Lipschitz Continuity -- the Strongly Convex Case19 Jan 2023
- 2022A Non-Asymptotic Moreau Envelope Theory for High-Dimensional Generalized Linear Models21 Oct 2022