Characterization of Lipschitz continuous DC functions
A. Hantoute, J. E. Mart\'inez-Legaz
TL;DR
This paper establishes a precise criterion for when difference of convex functions on locally convex spaces are Lipschitz continuous, based on epsilon-subdifferential intersections, advancing the theoretical understanding of DC functions.
Contribution
It provides a necessary and sufficient condition for Lipschitz continuity of DC functions using epsilon-subdifferential intersections, a novel theoretical result.
Findings
Characterization of Lipschitz continuous DC functions
Criterion based on epsilon-subdifferential intersections
Advances understanding of DC function regularity
Abstract
We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a locally convex space, to be Lipschitz continuous. Our criterion relies on the intersections of the "epsilon-subdifferentials of the involved functions.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Advanced Control Systems Optimization