Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization

TL;DR

This paper introduces a novel Quantum Hamiltonian Descent based Augmented Lagrangian Method for solving large-scale, constrained nonconvex nonlinear programming problems, demonstrating its effectiveness on a Power-to-Hydrogen System.

Contribution

It develops a new quantum-inspired optimization framework combining ALM and QHD, with a classical simulation approach, for complex NLP problems.

Findings

Successfully applied to Power-to-Hydrogen System

Verified effectiveness through simulation results

Addresses large-scale, nonconvex NLP challenges

Abstract

Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant challenge due to the complexity of the solution landscape and the presence of nonlinear nonconvex constraints. In this paper, we develop a Quantum Hamiltonian Descent based Augmented Lagrange Method (QHD-ALM) framework to address largescale, constrained nonconvex NLP problems. The augmented Lagrange method (ALM) can convert a constrained NLP to an unconstrained NLP, which can be solved by using Quantum Hamiltonian Descent (QHD). To run the QHD on a classical machine, we propose to use the Simulated Bifurcation algorithm as the engine to simulate the dynamic process. We apply our algorithm to a Power-to-Hydrogen System, and the simulation results verify the effectiveness of our algorithm.