Holder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions

• 成果类型: Article
• 署名作者: Thai Doan Chuong; Do Sang Kim
• 署名单位: Saigon University; Pukyong National University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0741
• 发表日期: 2016
• 页码: 596-611
• 关键词: subregularity; STABILITY; INEQUALITY; nonsmooth

摘要

We introduce concepts of metric regularity and metric subregularity of a positive-order for an implicit multifunction and provide new sufficient conditions for the implicit multifunctions to achieve the addressed properties. The conditions provided are presented in terms of the Frechet/Mordukhovich coderivative of the corresponding parametric multifunction formulated the implicit multifunction. We show that such sufficient conditions are also necessary for the metric regularity/subregularity of a positive-order of the implicit multifunction when the corresponding parametric multifunction is (locally) convex and closed. In this way, we establish criteria ensuring that an implicit multifunction is Holder-like and calm of a positive-order at a given point. As applications, we derive sufficient conditions in terms of coderivatives for a multifunction (resp., its inverse multifunction) to have the open covering property and the metric regularity/subregularity of a positive-order (resp., the Holder-like/calm property).