Abstract. For nonconvex quadratic optimization problems, calculation of global extreme value estimates on the basis of Lagrangian relaxation of the original problems is considered. On the boundary of the feasible region of the estimation problem, the functions of the problem are discontinuous, ill-conditioned, which imposes certain requirements on the computational algorithms. The paper presents a new approach taking into account these features, based on the use of conical regularizations of convex optimization problems. It makes it possible to construct an equivalent unconditional optimization problem, whose objective function is defined on the entire space of problem variables and satisfies the Lipschitz condition.

Keywords: quadratic optimization problem, Lagrangian relaxation, condition of non-negative definiteness of the matrix, conical regularization.