Global error bounds for piecewise convex polynomials

• 成果类型: Article
• 署名作者: Li, Guoyin
• 署名单位: University of New South Wales Sydney
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-011-0481-z
• 发表日期: 2013
• 页码: 37-64
• 关键词: d-gap functions; inequality systems; optimality conditions; condition number; extension; nonsmooth; PROGRAMS; THEOREM

摘要

In this paper, by examining the recession properties of convex polynomials, we provide a necessary and sufficient condition for a piecewise convex polynomial to have a Holder-type global error bound with an explicit Holder exponent. Our result extends the corresponding results of Li (SIAM J Control Optim 33(5):1510-1529, 1995) from piecewise convex quadratic functions to piecewise convex polynomials.