Distributed Trust-Region Method With First Order Models

Abstract

In this paper, we introduce the trust region concept for distributed optimization. A large class of globally convergent methods of this type is used efficiently in centralized optimization, both constrained and unconstrained. The methods of this class are built on the idea of modeling the objective function at each iteration and taking the new iteration as the minimizer of the model in a certain area, called the trust region. The trust region size, the minimization method and the model function depend on the properties of the objective function. In this paper we propose a general framework and concentrate on the first order methods, i.e., the gradient methods. Using the trust-region mechanism for generating the step size we end up with a fully distributed method with node varying step sizes. Numerical results presented in the paper demonstrate the efficiency of the proposed approach.