Non-convex quadratic optimization on a parallelepiped

The approximating-combinatorial method for solving optimization problems is used for the search for a global maximum of a quadratic function on a parallelepiped. The approximating functions in this method are majorants of an object function. The majorants are constructed on subsets of parallelepiped of admissible solutions. The method is based on a diagonal or block-diagonal $LDL^T$-factorization of a matrix of an object function.