Strictly convex separable optimization with linear equality constraints and bounded variables

In this paper, minimization problem with a separable strictly convex objective function subject to several linear equality constraints and bounds on the variables (box constraints) is considered. Such problems arise in manufacturing, facility location, resource allocation, engineering and economic applications, etc. A necessary and sufficient condition (characterization) is proved for a feasible solution to be the (unique) optimal solution of the considered problem. Primal-dual analysis of the proposed approach is made. Examples of some important separable strictly convex objective functions for the problem under consideration are presented.