The optimal design method of double-mass dynamic vibration absorbers (DVAs) is discussed with respect to the minimization of the maximum amplitude magnification factor. The performance of a double-mass DVA is superior to a single-mass DVA with the same mass ratio, although the design methods are still the subject of studies. The design optimizations of double-mass DVAs that are arranged in parallel or series are formulated precisely using an optimality criteria approach in which the optimal parameters are obtained as the numerical solutions of simultaneous algebraic equations. The primal equations are derived using Vieta’s formula with the assumption that the optimal design is realized with three resonant points of equal height. The additional equations are derived as the determinants of Jacobian matrices that are defined using the primal equations. After rearrangement, these formulations realize the direct numerical solution of the design optimization via the solution of simultaneous algebraic equations. Examples are provided that prove the effects of double-mass DVAs. The formulations used in this study are variants of the algebraic approach developed by the author that realized the closed-form algebraic exact solutions to a popular design optimization of a single-mass DVA. The well-known design formulae that use the fixed points by J. P. Den Hartog and J. E. Brock correspond to an approximate solution to this problem.