{"ID":2886043,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.02969","arxiv_id":"2508.02969","title":"Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization","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.","short_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 non...","url_abs":"https://arxiv.org/abs/2508.02969","url_pdf":"https://arxiv.org/pdf/2508.02969v1","authors":"[\"Mingze Li\",\"Lei Fan\",\"Zhu Han\"]","published":"2025-08-05T00:15:54Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}