Branch-and-bound method for the minimization problem for a nonconvex quadratic function under convex quadratic constraints (Q2713937)

The authors study the minimization problem for a quadratic function on a convex bounded set defined by quadratic and linear inequalities. To solve the problem, the authors propose a version of the branch-and-bound method in which, on each step, a set determined as the intersection of a finite set of ellipsoids is approximated by internal and external ellipsoids. Estimates for the optimal value of the goal function are found as solutions to a minimization problem of a quadratic function on the ball. Convergence of the method proposed is proven and estimates of the degree of convergence are obtained.