The nonlinear synthesis problems of antenna arrays according to the given amplitude radiation pattern (RP) are solved by the method which regards the mutual coupling of radiators. The mutual coupling is taken into account by solving the boundary problem of the high-frequency electrodynamics on the multi-connected areas. The variational formulation of problems is considered. It is reduced to solving the nonlinear integral or matrix equations – the Euler equations. The numerical algorithm of solving for optimum generation minimization sequence, which weakly convergences to the point of the local minimum is developed. The branching of solutions in the case of linear vibrators synthesis, is investigated by the methods of nonlinear analysis [1]. The number of solutions to these problems and their qualitative characteristics are dependent on both the electrical size of the array and the properties of the given RP.