Nondegeneracy concepts for zeros of piecewise smooth functions

• 成果类型: Article
• 署名作者: Sznajder, R; Gowda, MS
• 署名单位: University System of Maryland; Bowie State University; University System of Maryland; University of Maryland Baltimore County
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.23.1.221
• 发表日期: 1998
• 页码: 221-238
• 关键词: linear complementarity-problem; variational-inequalities; local-structure; feasible sets; STABILITY; CONVERGENCE; point; MAPS

摘要

A zero of a piecewise smooth function Sis said to be nondegenerate if the function is Frechet differentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational inequality problem corresponding to a polyhedral convex set. Some properties of nondegenerate zeros of piecewise affine functions are described. We generalize a recent result of Ferris and Pang on the existence of a nondegenerate solution of an affine variational inequality problem which itself is a generalization of a theorem of Goldman and Tucker.