### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 111-123 |

Journal | Mathematical programming |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1976 |

### Keywords

- IR-85459

### Cite this

*Mathematical programming*,

*10*(1), 111-123. https://doi.org/10.1007/BF01580656

}

*Mathematical programming*, vol. 10, no. 1, pp. 111-123. https://doi.org/10.1007/BF01580656

**Projections in minimax algebra.** / Cuninghame-Green, R.A.

Research output: Contribution to journal › Article › Academic

TY - JOUR

T1 - Projections in minimax algebra

AU - Cuninghame-Green, R.A.

PY - 1976

Y1 - 1976

N2 - An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, ⊕, ⊗), that is over the (extended) real numbersR with the binary operationsx ⊕ y = max (x,y) andx ⊗ y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality.

AB - An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, ⊕, ⊗), that is over the (extended) real numbersR with the binary operationsx ⊕ y = max (x,y) andx ⊗ y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality.

KW - IR-85459

U2 - 10.1007/BF01580656

DO - 10.1007/BF01580656

M3 - Article

VL - 10

SP - 111

EP - 123

JO - Mathematical programming

JF - Mathematical programming

SN - 0025-5610

IS - 1

ER -