### Abstract

The purpose of this paper is to study some recent applications of the n by dn LCP solvable by a parametric principal pivoting algorithm (PPP algorithm). Often, the LCPs arising from these applications give rise to large systems of linear equations which can be solved fairly efficiently by exploiting their special structures. First, it is shown that by analyzing the n by dn LCP we could study the problem of solving a system of equations and the (nonlinear) complementarity problem when the function involved is separable. Next, we examine conditions under which the PPP algorithm is applicable to a general LCP, and then present examples of LCPs arising from various applications satisfying the conditions; included among them is the n by dn LCP with a certain P-property. Finally we study a special class of n by dn LCPs which do not possess the P-property but to which the PPP algorithm is still applicable; a major application of this class of problems is a certain economic spatial equilibrium model with piecewise linear prices.

Original language | English |
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Pages (from-to) | 297-319 |

Number of pages | 23 |

Journal | Linear Algebra and Its Applications |

Volume | 34 |

Issue number | C |

DOIs | |

Publication status | Published - 1980 Dec |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

*Linear Algebra and Its Applications*,

*34*(C), 297-319. https://doi.org/10.1016/0024-3795(80)90170-6