Abstract. The author analyzes the conditions of obtaining exact solutions to quadratic extremum problems of general type by using SDP-relaxations. Based on the known results for exactness of dual bounds (lagrangian relaxations) and their relationship with SDP-relaxations, several conditions are formulated, under which the values of optimal objective function of the quadratic extremal problem and its SDP-relaxation are equal.

Keywords: quadratic extremal problem, SDP-relaxation, dual bound, lagrangian, exact relaxation.