On the Solution of a Nonconvex Fractional Quadratic Problem

In this paper, we give an algorithm for solving a class of nonconvex quadratic fractional problems that may arise during a correction of inconsistent set of linear inequalities. First, we show that for rank deficient matrices, an optimal solution for a nonconvex fractional minimization problem can be obtained via convex optimization approach. Then an iterative algorithm is designed to solve the problem in the full rank case. Finally, an illustrative numerical example is presented.