  We introduce a new stochastic differential model for global optimization of
nonconvex functions on compact hypersurfaces. The model is inspired by the
stochastic Kuramoto-Vicsek system and belongs to the class of Consensus-Based
Optimization methods. In fact, particles move on the hypersurface driven by a
drift towards an instantaneous consensus point, computed as a convex
combination of the particle locations weighted by the cost function according
to Laplace's principle. The consensus point represents an approximation to a
global minimizer. The dynamics is further perturbed by a random vector field to
favor exploration, whose variance is a function of the distance of the
particles to the consensus point. In particular, as soon as the consensus is
reached, then the stochastic component vanishes. In this paper, we study the
well-posedness of the model and we derive rigorously its mean-field
approximation for large particle limit.
