An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems.

In this paper, we study the problem of maximizing the sum of a concave–convex quadratic fractional function on a non-empty, bounded, convex quadratic feasible set, which is called the problem (QCQFP). By using a conventional semidefinite program (SDP) relaxation, QCQFP is reformulated as a class of linear fractional programming problems over the cone of positive semidefinite matrices, which we refer to these problems as SDFP. After expatiating the properties of SDFP, we transform SDFP into its equivalent problem (ESDFP) whose non-convexity is mainly reflected in the newly added nonlinear equality constraints. By relaxing these nonlinear equality constraints into linear constraints, a special SDP relaxation is generated for ESDFP. Based on these results, an effective branch-and-bound algorithm is designed, and its theoretical convergence and worst-case complexity are proved. Numerical experiments demonstrate that the proposed algorithm is effective and feasible. [ABSTRACT FROM AUTHOR]