Distributed and Asynchronous Algorithms for N-block Convex Optimization with Coupling Constraints

Abstract

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.

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• Solving Multiple-Block Separable Convex Minimization Problems Using Two-Block Alternating Direction Method of Multipliers
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• Parallel Direction Method of Multipliers