Minimization of a strictly convex separable function subject to a convex inequality constraint or linear equality constraints and bounds on the variables

In this paper, we consider the problem of minimizing a strictly convex separable function over a feasible region defined by a convex inequality constraint and two-sided bounds on the variables (box constraints). Also, the convex separable program with a strictly convex objective function subject to linear equality constraints and bounded variables is considered. These problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems and in various practical problems. Characterization theorems (necessary and sufficient conditions) for the optimal solution to the considered problems are proved. Some illustrative examples are also presented.