### Abstract

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.

Original language | Undefined |
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Pages (from-to) | 111-123 |

Journal | Mathematical programming |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1976 |

### Keywords

- IR-85459

## Cite this

Cuninghame-Green, R. A. (1976). Projections in minimax algebra.

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