The special case of  convex separable optimization is considered in this paper. Relations between an admissible solution and an optimal solution of the initial separable optimization problem (SP), approximate separable problem (ASP), and linear approximate separable problem (LASP) are considered. The problem of mesh (grid) point generation, which is important about accuracy of the approximation process for the separable problem, is also considered. Estimates of the accuracy of the particular piecewise linear approximation, which is used, are presented.