Mix-CALADIN: A Distributed Algorithm for Consensus Mixed-Integer Optimization

TL;DR

This paper introduces a new distributed algorithm for consensus mixed-integer optimization, especially Boolean variables, extending CALADIN with convergence guarantees for convex and nonconvex problems.

Contribution

It develops a novel distributed algorithm that handles Boolean variables without local solvers, with proven convergence under mild assumptions.

Findings

Achieves competitive performance in numerical experiments.

Provides rigorous convergence guarantees for both convex and nonconvex problems.

Extends the CALADIN framework to mixed-integer settings.

Abstract

This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian Alternating Direction Inexact Newton (CALADIN) framework by incorporating specialized techniques for handling Boolean variables without relying on local mixed-integer solvers. Under the mild assumption of Lipschitz continuity of the objective functions, we establish rigorous convergence guarantees for both convex and nonconvex mixed-integer programming problems. Numerical experiments demonstrate that the proposed algorithm achieves competitive performance compared to existing approaches while providing rigorous convergence guarantees.