Separable convex programs with ratio constraints over a directed tree

This paper describes a class of separable convex programs with ratio constraints over a directed tree that has applications in production planning, regression analysis, quality improvement, and other related areas. To develop a simple procedure for solving this class of problems, the authors extend the procedure for solving separable convex programs with partially ordered variables. For any problem that has N variables, the present simple procedure finds an optimal solution by solving at most 2N convex subproblems with one variable.