Consensus-based parallel algorithm for robust convex optimization with scenario approach in colored network

Abstract

This paper mainly proposes an parallel distributed learning algorithm for the robust convex optimization (RCO). Firstly, the scenario approach is used to transform RCO into its probabilistic approximation Scenario Problem (SP), which is distributively solved by multiprocessors to lighten the computational burden. Secondly, each processor (node) of the colored network processes the local optimization via a primal-dual subgradient algorithm (PDSA) to obtain an optimal solution called a local variable. Finally, a consensus method named the Colored Distributed Average Consensus (CDAC), which is based on Distributed Average Consensus (DAC), is proposed to act on the whole local variables to obtain the global optimal solution. Experimental results show that CDAC has an advantage in terms of computational time over DAC, while they have the same results.