DualBi: A dual bisection algorithm for non-convex problems with a scalar complicating constraint

TL;DR

This paper introduces DualBi, an iterative dual bisection algorithm for non-convex problems with a scalar constraint, enabling decentralized solutions especially in multi-agent MILPs, with improved performance over existing methods.

Contribution

The paper presents a novel dual bisection algorithm that efficiently solves non-convex problems with scalar constraints and facilitates decentralized multi-agent optimization.

Findings

Demonstrates improved convergence over state-of-the-art methods

Provides a decentralized scheme for multi-agent problems

Shows effectiveness in multi-agent MILP simulations

Abstract

This paper addresses non-convex constrained optimization problems that are characterized by a scalar complicating constraint. We propose an iterative bisection method for the dual problem (DualBi Algorithm) that recovers a feasible primal solution, with a performance that is progressively improving throughout iterations. Application to multi-agent problems with a scalar coupling constraint results in a decentralized resolution scheme where a central unit is in charge of the update of the (scalar) dual variable while agents compute their local primal variables. In the case of multi-agent MILPs, simulations showcase the performance of the proposed method compared with state-of-the-art duality-based approaches.