  We propose a method of bi-coordinate variations for non-stationary and
non-smooth optimization problems, which involve a single linear equality and
box constraints. Here only approximation sequences are known instead of exact
values of the cost function and parameters of the feasible set. It consists in
making descent steps with respect to only two selected coordinates satisfying
some special threshold rule. The method is simpler essentially than the usual
gradient or dual type ones and differs from the previous known bi-coordinate
ones suggested for the usual stationary and smooth problems. We establish its
convergence under rather mild assumptions. Computational tests also reveal
certain preferences of the proposed method over the known ones.
