Minimization of a strictly convex separable function subject to convex separable inequality constraint and box constraints

A minimization problem with strictly convex separable objective function subject to a convex separable inequality constraint of the form "less than or equal to" and bounds on the variables is considered. Necessary and sufficient condition is proved for a feasible solution to be an optimal solution to this problem. An iterative algorithm of polynomial complexity for solving such problems is suggested and its convergence is proved. Modifications of this algorithm are proposed in connection with some extensions of the considered problem as well as in order to avoid some computational difficulties. Examples of important convex functions for the problem under consideration and computational results are presented.