A complementarity partition theorem for multifold conic systems

• 成果类型: Article
• 署名作者: Pena, Javier; Roshchina, Vera
• 署名单位: Carnegie Mellon University; Federation University Australia; University of Evora
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0577-0
• 发表日期: 2013
• 页码: 579-589
• 关键词: complexity theory

摘要

Consider a homogeneous multifold convex conic system Ax = 0, x is an element of K-1 x ... x K-r and its alternative system A(T) y is an element of K-1* x ... x K-r*, where K-1, ... , K-r are regular closed convex cones. We show that there is a canonical partition of the index set {1, ... , r} determined by certain complementarity sets associated to the most interior solutions to the two systems. Our results are inspired by and extend the Goldman-Tucker Theorem for linear programming.