Generalized Monotonicity and the Proximal Point Algorithm

• 成果类型: Article; Early Access
• 署名作者: Luke, D. Russell; Tam, Matthew K.
• 署名单位: University of Gottingen; University of Melbourne
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2025.0863
• 发表日期: 2025-11-21
• 关键词: generalized monotonicity; proximal point algorithm; metric subregularity; almost a-firmly nonexpansive; submonotone; differentiability; regularization; CONVERGENCE; convexity; Operators

摘要

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.