Global optimization for sum of linear ratios problem with coefficients

The global optimization of the sum of linear ratios problem has attracted the interest of researchers and practitioners for a number of years. Since these types of optimization problems are nonconvex, various specialized algorithms have been proposed for globally solving these problems. However, these algorithms are only for the case that sum of linear ratios problem without coefficients, and may be difficult to implement. In this paper, a branch and bound algorithm is proposed for globally solving the sum of linear ratios problem with coefficients. By utilizing an equivalent problem and linearization technique, the initial nonconvex programming problem is reduced to a sequence of linear programming problems. The proposed algorithm is convergent to the global optimal solution by means of the subsequent solutions of a series of linear programming problems. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.