Uniqueness for solutions of differential complementarity problems

• 成果类型: Article
• 署名作者: Stewart, David E.
• 署名单位: University of Iowa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0195-4
• 发表日期: 2009
• 页码: 327-345
• 关键词: linear transformations; p-properties

摘要

In this paper we consider the question of which matrices M give unique solutions for Differential Complementarity Problems (Mandelbaum 1989, unpublished manuscript) of the form dw/dt = Mz + q(t), w(0) = w(0) K ?? z(t) perpendicular to w(t) is an element of K* for all t, for all q and w(0) is an element of K* where K is a closed convex cone. Explicit descriptions of the set of such matrices are given for the 2 x 2 case; the set of such M's independent of K is a strict subset of the set of positive definite matrices (nu(T) M nu > 0 for all nu not equal 0) but strictly contains the set of symmetric positive definite matrices. These results have implications for a range of different formulations of dynamic systems with complementarity constraints.