Maximizing for the sum of ratios of two convex functions over a convex set
This paper presents an algorithm for globally maximizing a sum of convex-convex ratios problem with a convex feasible region, which does not require involving all the functions to be differentiable and requires that their sub-gradients can be calculated efficiently. To our knowledge, little progress has been made for globally solving this problem so far. The algorithm uses a branch and bound scheme in which the main computational effort involves solving a sequence of linear programming subproblems. Because of these properties, the algorithm offers a potentially attractive means for globally solving the sum of convex-convex ratios problem over a convex feasible region. It has been proved that the algorithm possesses global convergence. Finally, the numerical experiments are given to show the feasibility of the proposed algorithm. (C) 2013 Elsevier Ltd. All rights reserved.
sum of ratios branch and bound fractional programming global optimization