Constraints for the phase of a scattering amplitude from elastic unitarity

The constraints for the phase phi(x) of a scattering amplitude F(x) following from elastic unitarity are derived if its imaginary part in the forward direction and its absolute value [F(x)] are given. These constraints are obtained by applying the theory of nonlinear optimization. The relation of these results to the question of the uniqueness of the solutions of the elastic unitarity equation is discussed in detail. (Auth.)