A parallel computing scheme for minimizing a class of large scale functions
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.
function with partially separable variables
scientific article; zbMATH DE number 4113869
scientific article