Metric regularity of semi-infinite constraint systems

• 成果类型: Article
• 署名作者: Cánovas, MJ; Dontchev, L; López, MA; Parra, J
• 署名单位: Universidad Miguel Hernandez de Elche; Universitat d'Alacant
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-005-0618-z
• 发表日期: 2005
• 页码: 329-346
• 关键词: stability; optimization; distance

摘要

We obtain a formula for the modulus of metric regularity of a mapping defined by a semi-infinite system of equalities and inequalities. Based on this formula, we prove a theorem of Eckart-Young type for such set-valued infinite-dimensional mappings: given a metrically regular mapping F of this kind, the infimum of the norm of a linear function g such that F+g is not metrically regular is equal to the reciprocal to the modulus of regularity of F. The Lyusternik-Graves theorem gives a straightforward extension of these results to nonlinear systems. We also discuss the distance to infeasibility for homogeneous semi-infinite linear inequality systems.