Reducing separable convex programs with tree constraints

This paper describes a class of separable convex programs with tree constraints that has applications in production planning, quality improvement, and other related areas. A reduction procedure is presented for solving this class of separable convex programs with N variables. This reduction procedure determines an optimal solution to the convex problem by solving at most 2N simple convex subproblems with one variable. Hence, this reduction procedure is an efficient approach for solving large scale convex programs of this sort.