The reconfigurable intelligent surface (RIS) has brought a revolutionary paradigm to wireless communication, allowing unprecedented opportunities towards enhancing signal quality and coverage. An attempt towards solving the issues related to multi-beam design in the near-field scenarios of RIS is made in this paper. A new multi-beam design framework based on an Alternating Direction Method of Multipliers (ADMM) is proposed for the optimization of the beamforming process. It is compared in simulation, with established approaches such as Block Coordinate Descent combined (BCD) with Majorization-Minimization (MM), with regard to both convergence rates and communication performance. Our results show that the ADMM algorithm converges much faster and is more efficient than classical approaches. Hence, this promising solution can be considered for future communication systems which will support RIS.