The application of the nonlinearly constrained optimization method to low sidelobe synthesis of the space-scanned axial dipole arrays on cylindrical surfaces is discussed inthis paper.By adopting the information of the array element realized gain patterns

we propose an approximation method for finding the maximal sidelobe level of the scanned pattern with the prespecified beam pointing

and formulate the synthesis problem of the scanned arrays with the specified scan angle as nonlinearly constrained optimization problems. By using the new direct method

we can find a set of array coefficients that yield a scanned pattern

with the specified scan angle

meeting the specified sidelobe level and maximizing the directivity

if such a set of array coefficients exists.When the sidelobe specification can not be met

we can find a set of array coefficients that yield a scanned pattern meeting the best attainable sidelobe level and maximizing the directivity. Also

some numerical results for the low sidelobe control of the space-scanned axial dipole arrays on cylindrical surfaces are given.