Characterization of the optimal solution of the convex generalized nonlinear transportation problem

A convex generalized nonlinear transportation problem is considered in this paper. A necessary and sufficient optimality condition (characterization theorem) for a feasible solution to be an optimal solution to this problem is formulated and proved. The convex generalized nonlinear transportation problem with bounds on the variables is also considered, and characterization theorem for this problem is stated and proved. Examples of some (strictly) convex objective functions for the considered problems are presented, and open problems for future research are stated.