On solving quadratically constrained quadratic programming problem with one non-convex constraint

In this paper we consider a quadratically constrained quadratic programming problem with convex objective function and many constraints in which only one of them is non-convex. This problem is transformed to a parametric quadratic programming problem without any non-convex constraint and then by solving the parametric problem via an iterative scheme and updating the parameter in each iteration, the solution of the problem is achieved. The convergence of the proposed method is investigated. Numerical examples are given to show the applicability of the new method. © 2018, Operational Research Society of India.