Active-Set Newton Methods and Partial Smoothness

• 成果类型: Article
• 署名作者: Lewis, Adrian S.; Wylie, Calvin
• 署名单位: Cornell University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2020.1075
• 发表日期: 2021
• 页码: 712-725
• 关键词: local linear convergence; proximal points; identification

摘要

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active-set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.