Comp. Appl. Math. DOI 10.1007/s40314-014-0199-7 Parametric approach for solving quadratic fractional optimization with a linear and a quadratic constraint Maziar Salahi · Saeed Fallahi Received: 13 May 2014 / Revised: 27 September 2014 / Accepted: 19 October 2014 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014 Abstract This paper studies a class of nonconvex fractional minimization problem in which the feasible region is the intersection of the unit ball with a single linear inequality con- straint. First, using Dinkelbach’s idea, it is shown that finding the global optimal solution of the underlying problem is equivalent to find the unique root of a function. Then using a diag- onalization technique, we present an efficient method to solve the indefinite quadratic mini- mization problem with the original problem’s constraints within a generalized Newton-based iterative algorithm. Our preliminary numerical experiments on several randomly generated test problems show that the new approach is much faster in finding the global optimal solu- tion than the known semidefinite relaxation approach, especially when solving large-scale problems. Keywords Fractional optimization · Extended trust region subproblems · Global optimization · Generalized Newton method · Semidefinite optimization relaxation Mathematics Subject Classification 90C32 · 90C26 · 90C22 1 Introduction Consider the following quadratic fractional problem (QFP) min x T A 1 x + b T 1 x + c 1 x T A 2 x + b T 2 x + c 2 (QFP) Communicated by Natasa Krejic. M. Salahi (B ) · S. Fallahi Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran e-mail: salahim@guilan.ac.ir; salahi.maziar@gmail.com S. Fallahi e-mail: saeedf808@gmail.com 123