# A Geometric Problem in Simplicial Cones with Applications to Linear Complementarity Problems

1986) A Geometric Problem in Simplicial Cones with Applications to Linear Complementarity Problems. Technical Report TR-86-29, Computer Science, Virginia Polytechnic Institute and State University. (

Full text available as: |

## Abstract

We consider the following geometric question: suppose we are given a simplicial cone K in R^n. Can we find a point @) in the interior of K satisfying the property that the orthogonal projection of @) onto the linear hull of every face of K is in the relative interior of that fence? This question plays an important role in determining whether a certain class of linear complementarity problems (LCP 's) can be solved efficiently by a pivotal algorithm. The answer to this question is always in the affirmative if n=2, but not so for n=3. We establish some conditions for the answer to this question to be yes, and relate them to other well known properties of square matrices. e.g., world: simplicial cones, orthogonal projections, faces, linear complementarity problem, LCP, pivotal algorithms, P-matrices, symmetric positive definite matrices, 2-matrices, M-matrices.

Item Type: | Departmental Technical Report |
---|---|

Subjects: | Computer Science > Historical Collection(Till Dec 2001) |

ID Code: | 36 |

Deposited By: | User autouser |

Deposited On: | 03 November 2005 |