Convex programs based on the Young inequality and its relation to linear programming

In this paper the a class of convex programming problem is introduced based on the Young inequality. Therefore we call this convex programs Young programming. The Young programming is an analytical approximation of linear programming. A perfect dual of the Young programming problem is formulated. An algorithm is presented for the solution of Young programming problems which is shown to be a row-action method in terms of the primal problem and a sequence of one dimensional minimization problems, we call it dir-action method, in terms of the dual problem.