Generalized Monotonicity and the Proximal Point Algorithm
Year: 2025
Type: article
Abstract: We study the proximal point algorithm when the operator of interest is metrically subregular and satisfies a submonotonicity property. The latter property can be viewed as a quantified weakening of the standard definition of a monotone operator. Our main result gives a condition under which locally, the proximal point algorithm generates sequences that are linearly convergent to a zero of the underlying operator. General properties of our notion of submonotonicity are also explored as well as connections to other concepts in the literature. Funding: D. R. Luke was supported in part by the Deutsche Forschungsgemeinschaft [Grants 541767835 and SFB1456/1-432680300]. M. K. Tam was supported in part by the Australian Research Council [Grant DP230101749].
Authors: D. Russell Luke, Matthew K. Tam
Institutions: University of Göttingen, The University of Melbourne
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416512437