Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908478731190272 |
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| author | Li, Mingze Fan, Lei Han, Zhu |
| author_facet | Li, Mingze Fan, Lei Han, Zhu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization Li, Mingze Fan, Lei Han, Zhu Optimization and Control Systems and Control 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. |
| title | Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2508.02969 |