General Return Mapping in the softening regime

The interpretation of general return mapping integration algorithm as closest point projection of the trial stress state leads to a lagragian with arguments as the state of the system. In the hardening regime, this lagragian is convex and newton's method guarantee uniqueness and convergence (Simo and Hughes). I am interested in the case when the lagragian is no longer definetively convex as could be the case in softening regime. Can anybody suggest me numerical techniques for this case?