Conditions for the existence, identification and calculus rules of the threshold of prox-boundedness
Publication Name
Optimization Letters
Abstract
This note advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite dimensions, we study general prox-bounded functions and then focus on some useful classes such as piecewise functions and Lipschitz continuous functions. The thresholds are explicitly determined when possible and bounds are established otherwise. Some calculus rules are constructed; we consider functions with known thresholds and find the thresholds of their sum and composition.
Open Access Status
This publication is not available as open access
Volume
15
Issue
1
First Page
45
Last Page
57