标题： 基于量子哈密顿下降的增广拉格朗日方法用于约束非凸非线性优化 显示英文标题

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

摘要： 非线性规划（NLP）在电力能源系统、化学工程、通信网络和金融工程等领域起着关键作用。 然而，由于解空间的复杂性和非线性非凸约束的存在，求解大规模非凸NLP问题仍然是一个重大挑战。 在本文中，我们开发了一个基于量子哈密顿下降的增广拉格朗日方法（QHD-ALM）框架，以解决大规模的有约束非凸NLP问题。 增广拉格朗日方法（ALM）可以将有约束的NLP转换为无约束的NLP，这可以通过使用量子哈密顿下降（QHD）来求解。 为了在经典计算机上运行QHD，我们提出使用模拟分叉算法作为引擎来模拟动态过程。 我们将算法应用于一个制氢系统，并且仿真结果验证了算法的有效性。 显示英文摘要

摘要： 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.