A global optimization algorithm for sum of quadratic ratios problem with coefficients

In this paper a global optimization algorithm for solving sum of quadratic ratios problem with coefficients and nonconvex quadratic function constraints (NSP) is proposed. First, the problem NSP is converted into an equivalent sum of linear ratios problem with nonconvex quadratic constraints (LSP). Using a linearization technique, the linearization relaxation problem of LSP is obtained. The original problem is then solvable using the branch and bound method. In the algorithm, lower bounds are derived by solving a sequence of linear lower bounding functions for the objective function and the constraint functions of the problem NSP over the feasible region. The proposed algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems. The numerical examples demonstrate that the proposed algorithm can easily be applied to solve problem NSP.