A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the sparsity of the involved matrices and solves the problem via solving a sequence of positive definite system of linear equations after identifying suitable generalized eigenvalues. Specifically, we analyze how to recognize hard case (case 2) in a preprocessing step, fixing an error in Sect.2.2.2 of Pong and Wolkowicz (Comput Optim Appl 58(2):273-322, 2014) which studies the same problem with the two-sided constraint. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with some recent algorithms in the literature.