A parallel computing scheme for minimizing a class of large scale functions
type: Item
instance of: scholarly article
title: A parallel computing scheme for minimizing a class of large scale functions
zbMATH Open document ID: 0679.65040
DOI: 10.1016/0096-3003(89)90055-6
author: Renpu Ge
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: This paper deals with the problem of globally minimizing over \({\mathbb{R}}^ n\) functions of the form \[ f(x)=\sum^{m}_{i=1}f_ i(x_ i)+\sum^{m}_{i=1}\sum_{j>i}f_{ij}(x_ i,x_ j), \] where \(x_ i\in {\mathbb{R}}^{n(i)}\) (1\(\leq i\leq m)\), \(f_ i\) is twice continuously differentiable and \(f_{ij}\) is bilinear. An algorithm of solving this problem is presented and it is shown that, under some conditions, it converges with a specific relative convergence rate. Also, it is proved that the algorithm can be adapted for solving systems of homogeneous equations in which the right-hand-side functions have forms similar with f above.
reviewed by: Dan Butnariu
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4113869
zbMATH Keywords: parallel computing scheme
zbMATH Keywords: large scale functions
zbMATH Keywords: function with partially separable variables
zbMATH Keywords: global minimization
zbMATH Keywords: algorithm
zbMATH Keywords: convergence rate
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90055-6
OpenAlex ID: W2095353962
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description: scientific article; zbMATH DE number 4113869