Evaluating the solution performance of the augmented Lagrangian function on Ising machines
Abstract
We apply the augmented Lagrangian function (ALF) as a formulation for Ising machines and evaluate its performance by time-to-epsilon (\mathrm{TT\varepsilon}). The ALF has been well studied in continuous optimization for its numerical stability and convergence, and its advantage over the penalty function formulation is demonstrated here through the following results. Using the quadratic knapsack problem as a benchmark, we examine the dependence of \mathrm{TT\varepsilon} on the hyperparameters μand λ. The augmented Lagrangian formulation reduces \mathrm{TT\varepsilon} by roughly an order of magnitude compared with the penalty function formulation, keeping μsmall while obtaining feasible solutions and, for representative parameter settings, reaching high-precision solutions earlier in the search. These findings indicate that the augmented Lagrangian function is a promising formulation for improving the solution performance of Ising machines.
Versions
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BibTeX
@misc{awai2026evaluating,
title = {{Evaluating the solution performance of the augmented Lagrangian function on Ising machines}},
author = {Shunsuke Awai and Takuro Itoh and Keita Takahashi and Kotaro Tanahashi and Shu Tanaka},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.24241},
eprint = {2606.24241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24241},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evaluating the solution performance of the augmented Lagrangian function on Ising machines
AU - Shunsuke Awai
AU - Takuro Itoh
AU - Keita Takahashi
AU - Kotaro Tanahashi
AU - Shu Tanaka
PY - 2026
DA - 2026/06/23
PB - arXiv
DO - 10.48550/arxiv.2606.24241
UR - https://arxiv.org/abs/2606.24241
AB - We apply the augmented Lagrangian function (ALF) as a formulation for Ising machines and evaluate its performance by time-to-epsilon (\mathrm{TT\varepsilon}). The ALF has been well studied in continuous optimization for its numerical stability and convergence, and its advantage over the penalty function formulation is demonstrated here through the following results. Using the quadratic knapsack problem as a benchmark, we examine the dependence of \mathrm{TT\varepsilon} on the hyperparameters μand λ. The augmented Lagrangian formulation reduces \mathrm{TT\varepsilon} by roughly an order of magnitude compared with the penalty function formulation, keeping μsmall while obtaining feasible solutions and, for representative parameter settings, reaching high-precision solutions earlier in the search. These findings indicate that the augmented Lagrangian function is a promising formulation for improving the solution performance of Ising machines.
ER -