Vector Compact Summation with Greedy Algorithm

Author: Giorgi Chelidze
Keywords: vector compact summation, greedy algorithm
Annotation:

We show that in any two-dimensional linear normed space there exists a collection of vectors x_1,x_2,…,x_n, such that the greedy algorithm for estimation of 〖min〗_π 〖max〗_(1≤k≤n) ||∑_(i=1)^k▒x_(π(i)) || fails to be optimal.