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<p>In the paper, the orthogonal-constrained optimization problem for computing the ground states of the quasi-1D Gross-Pitaevskii equation (GPE) is considered. The results of calculating this optimization problem using the traditional Newton-augmented Lagrangian method are not consistent with the physical interpretation and are sensitive to the parameters. To overcome the drawback, a nonmonotonic algorithm combining Barzilai-Borwein(BB) step size is proposed, which is a modification of the proximal augmented Lagrange algorithm proposed by Gao et al. (SIAM J. Sci. Compot. 41 (3), A1949-A1983, 2019). Then, the global convergence and Q-linear convergence of the algorithm are derived, under some specific conditions. Finally, we demonstrate that the algorithm is effective and stable by numerical experiments on quasi-1D GPE problems.</p>

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A Nonmonotonic Algorithm for Computing the Ground States of a Quasi-1D Dipolar Bose-Einstein Condensates

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Shu-Jing Yang,
  • Lu-Bin Cui,
  • Xin-Guang Yang,
  • Alain Miranville,
  • Xing-Dong Zhao,
  • Jin-Yun Yuan

摘要

In the paper, the orthogonal-constrained optimization problem for computing the ground states of the quasi-1D Gross-Pitaevskii equation (GPE) is considered. The results of calculating this optimization problem using the traditional Newton-augmented Lagrangian method are not consistent with the physical interpretation and are sensitive to the parameters. To overcome the drawback, a nonmonotonic algorithm combining Barzilai-Borwein(BB) step size is proposed, which is a modification of the proximal augmented Lagrange algorithm proposed by Gao et al. (SIAM J. Sci. Compot. 41 (3), A1949-A1983, 2019). Then, the global convergence and Q-linear convergence of the algorithm are derived, under some specific conditions. Finally, we demonstrate that the algorithm is effective and stable by numerical experiments on quasi-1D GPE problems.