Pc-matrices and the linear complementarity problem
- Resource Type
- Authors
- Menglin Cao; Michael C. Ferris
- Source
- Linear Algebra and its Applications. 246:299-312
- Subject
- Discrete mathematics
Numerical Analysis
Class (set theory)
Algebra and Number Theory
Solution set
Lemke's algorithm
Linear complementarity problem
Piecewise linear function
Matrix (mathematics)
Complementarity theory
Discrete Mathematics and Combinatorics
Geometry and Topology
Mixed complementarity problem
Mathematics
- Language
- ISSN
- 0024-3795
We introduce a new matrix class Pc, which consists of those matrices M for which the solution set of the corresponding linear complementarity problem is connected for every q ϵ Rn. We consider Lemke's pivotal method from the perspective of piecewise linear homotopies and normal maps and show that Lemke's method processes all matrices in Pc ∩ Q0. We further investigate the relationship of the class Pc to other known matrix classes and show that column sufficient matrices are a subclass of Pc, as are 2 × 2 P0-matrices.