FINDING AN EXTREMUM IN A NONREGULAR GRID PROBLEM WITH FIXED EXTRA PAYMENTS WHEN THERE ARE LOSSES.

An examination is made of a method of solving a grid problem of concave programming with fixed extra payments and the presence of losses of a flow. The method ensures that the extremum of the target function will be found by linear programming, without the introduction of supplementary integer-valued variables. Losses of the flow in the grid are taken into account by an equivalent change in the gradient of the piecewise-linear target function, with estimation of the influence of losses in the preceding arcs on the gradients of subsequent arcs of the inverted grid. As a particular example, application of the method is illustrated for solving a grid problem.