### Abstract

The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0, ż ≥ 0, w^{T}ż = 0, where a dot denotes the derivative with respect to the scalar parameter t ≥ 0. In this problem, q, p are n-vectors with q ≥ 0 and M is a n by n P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.

Original language | English |
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Pages (from-to) | 146-154 |

Number of pages | 9 |

Journal | Mathematical Programming |

Volume | 15 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1978 Dec |

Externally published | Yes |

### Fingerprint

### Keywords

- Linear Complementarity Problem
- Principal Pivoting Algorithm

### ASJC Scopus subject areas

- Applied Mathematics
- Mathematics(all)
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research
- Software
- Computer Graphics and Computer-Aided Design
- Computer Science(all)

### Cite this

*Mathematical Programming*,

*15*(1), 146-154. https://doi.org/10.1007/BF01609013

**A parametric linear complementarity problem involving derivatives.** / Kaneko, Ikuyo.

Research output: Contribution to journal › Article

*Mathematical Programming*, vol. 15, no. 1, pp. 146-154. https://doi.org/10.1007/BF01609013

}

TY - JOUR

T1 - A parametric linear complementarity problem involving derivatives

AU - Kaneko, Ikuyo

PY - 1978/12

Y1 - 1978/12

N2 - The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0, ż ≥ 0, wTż = 0, where a dot denotes the derivative with respect to the scalar parameter t ≥ 0. In this problem, q, p are n-vectors with q ≥ 0 and M is a n by n P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.

AB - The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0, ż ≥ 0, wTż = 0, where a dot denotes the derivative with respect to the scalar parameter t ≥ 0. In this problem, q, p are n-vectors with q ≥ 0 and M is a n by n P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.

KW - Linear Complementarity Problem

KW - Principal Pivoting Algorithm

UR - http://www.scopus.com/inward/record.url?scp=0010120112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010120112&partnerID=8YFLogxK

U2 - 10.1007/BF01609013

DO - 10.1007/BF01609013

M3 - Article

AN - SCOPUS:0010120112

VL - 15

SP - 146

EP - 154

JO - Mathematical Programming

JF - Mathematical Programming

SN - 0025-5610

IS - 1

ER -