Ge, R.
(1989).
*A parallel computing scheme for minimizing a class of large scale functions.*
Applied Mathematics and Computation 30 (3) 261-288. 10.1016/0096-3003(89)90055-6.

## Abstract

This paper gives a parallel computing scheme for minimizing a twice continuously differentiable function with the form ƒf(x) = ∑i = 1mƒi(xi) + ∑i = 1m∑j = 1(j > i)m ƒij(xi, xj),where x = (xT1,…,xTm)T and xi ∈ Rni, ∑mi = 1ni = n, and n a very big number. It is proved that we may use m parallel processors and an iterative procedure to find a minimizer of ƒ(x). The convergence and convergence rate are given under some conditions. The conditions for finding a global minimizer of ƒ(x by using this scheme are given, too. A similar scheme can also be used parallelly to solve a large scale system of nonlinear equations in the similar way. A more general case is also investigated.

Item Type: | Article |
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Research Programs: | System and Decision Sciences - Core (SDS) |

Depositing User: | Luke Kirwan |

Date Deposited: | 09 Aug 2016 07:55 |

Last Modified: | 27 Aug 2021 17:41 |

URI: | http://pure.iiasa.ac.at/13623 |

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