Totally Asynchronous Primal-Dual Convex Optimization in Blocks

In this article, we present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The is “block-based,” in which vectors of primal and dual variables are partitioned into blocks, each updated only by single processor. We consider four behaviors that could be asynchronous: 1) updates to variables; 2) 3) communications 4) variables. show any amount asynchrony the can preclude convergence, though other forms permitted. A first-order update law then developed shown robust these asynchrony. next derive convergence rates an approximate Lagrangian saddle point terms operations agents execute, without specifying timing or pattern with they must executed. distance between solution obtain exact explicitly bounded. Convergence include “asynchrony penalty” quantify ways mitigate. Numerical results illustrate developments.