A nonlinear extension of Hoffman's error bounds for linear inequalities

• 成果类型: Article
• 署名作者: Zalinescu, C
• 署名单位: Martin Luther University Halle Wittenberg
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• 发表日期: 2003
• 页码: 524-532
• 关键词: convex; MULTIFUNCTIONS; systems

摘要

In a recent paper Li and Singer (1998) introduced the notion of global error bound for a convex multifunction at a point of its domain. They showed the existence of such a global error bound when the-image of the multifunction at the respective point is bounded and conjectured a result for the case when the image is not bounded. In this paper we solve their conjecture with a positive answer. For this we establish a criterion for the existence of a global error bound using the Pompeiu-Hausdorff excess. We also improve slightly some results of Li and Singer and introduce a gage associated to a multifunction similar to that for well-conditioning of convex functions, with similar properties.