Two parallel distribution algorithms for convex constrained minimization problems

A parallel gradient distribution (PGD) approach for minimizing a nonsmooth convex function on a block-separable convex set X of Rn and a parallel variable distribution (PVD) approach for minimizing a nonsmooth convex function on an inseparable closed convex set X of Rn are presented, which are constructed by using the Moreau–Yosida regularization of the convex functions. The convergence analysis for the two approaches is given as well.