Distributed Interval Optimization with Stochastic Zeroth-order Oracle

TL;DR

This paper introduces a stochastic zeroth-order algorithm for distributed interval optimization over dynamic networks, providing convergence guarantees and demonstrating effectiveness through numerical experiments.

Contribution

It proposes a novel stochastic zeroth-order method for distributed interval optimization with convergence analysis and practical validation.

Findings

Algorithm converges in expectation

Achieves Pareto optimal solutions

Effective in numerical simulations

Abstract

In this paper, we investigate a distributed interval optimization problem which is modeled with optimizing a sum of convex interval-valued objective functions subject to global convex constraints, corresponding to agents over a time-varying network. We first reformulate the distributed interval optimization problem as a distributed constrained optimization problem by scalarization. Then, we design a stochastic zeroth-order algorithm to solve the reformulated distributed problem, optimal solutions of which are also proved to be Pareto optimal solutions of the distributed interval optimization problem. Moreover, we construct the explicit convergence and the convergence rate in expectation of the given algorithm. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.