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We propose a method of bi-coordinate variations for non-stationary andnon-smooth optimization problems, which involve a single linear equality andbox constraints. Here only approximation sequences are known instead of exactvalues of the cost function and parameters of the feasible set. It consists inmaking descent steps with respect to only two selected coordinates satisfyingsome special threshold rule. The method is simpler essentially than the usualgradient or dual type ones and differs from the previous known bi-coordinateones suggested for the usual stationary and smooth problems. We establish itsconvergence under rather mild assumptions. Computational tests also revealcertain preferences of the proposed method over the known ones.

Selective Bi-coordinate Method for Non-Stationary and Non-Smooth Resource Allocation Type Problems