Variational Conditions Under the Constant Rank Constraint Qualification

• 成果类型: Article
• 署名作者: Lu, Shu
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1090.0431
• 发表日期: 2010
• 页码: 120-139
• 关键词: sensitivity-analysis; nonlinear programs; normal maps; inequalities; EQUATIONS; sets

摘要

This paper studies solution properties of a parametric variational condition under the constant rank constraint qualification (CRCQ), and properties of its underlying set. We start by showing that if the CRCQ holds at a point in a fixed set, then there exists a one-to-one correspondence between the collection of nonempty faces of the normal cone to the set at that point and the collection of active index sets at points nearby. We then study the behavior of the Euclidean projector, and prove under the CRCQ that the set of multipliers associated with the Euclidean projection is locally a continuous multifunction. Following that, we apply the degree theory to a localized normal map, to show that the combination of the CRCQ and the so-called strong coherent orientation condition suffices for the parametric variational condition to have a locally unique, continuous solution, which is selected from finitely many C-1 functions. Applications of this result under additional assumptions extend or recover some earlier results on parametric variational inequalities.