Exact Dual Bounds for Some Nonconvex Minimax Quadratic Optimization Problems

The nonconvex separable minimax quadratic optimization problem is analyzed. Two approaches to the problem solution are described, namely, by using SOCP relaxation and by using Lagrangian relaxation of a quadratic extremum analog problem. A condition is obtained that guarantees finding the value and the global extremum point of the problem of the considered class by calculating the dual bound of the equivalent quadratic extremum problem.