On non-convex quadratic optimization

This paper considers the search for the global minimization of non-convex functions, in particular, quadratic functions with non-definite matrix on a parallelepiped. The global search strategy is based on the global optimality conditions connected with the classical extremum theory and is in a non-trivial combination of linearized over basic non-convexity problems, local descent problems, problems of approximation of the convex functions level surfaces, and the one-dimensional search. Various numerical calculations have been carried out, to verify the algorithm effectivity.