  This paper first proposes an N-block PCPM algorithm to solve N-block convex
optimization problems with both linear and nonlinear constraints, with global
convergence established. A linear convergence rate under the strong
second-order conditions for optimality is observed in the numerical
experiments. Next, for a starting point, an asynchronous N-block PCPM algorithm
is proposed to solve linearly constrained N-block convex optimization problems.
The numerical results demonstrate the sub-linear convergence rate under the
bounded delay assumption, as well as the faster convergence with more
short-time iterations than a synchronous iterative scheme.
