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<p>We propose a novel Riemannian simulated annealing-based Barzilai–Borwein (RSABB) gradient method for optimization on manifolds. This hybrid approach combines the Barzilai–Borwein (BB) gradient method with a simulated annealing (SA) rule, tailored for optimization problems on the Stiefel manifold. The BB step size we utilize possesses a two-dimensional quadratic termination property. The proposed RSABB gradient method accepts the BB step according to SA rule, resulting in a new nonmonotone line search technique. If the BB step is not accepted, an Armijo line search is employed instead. Under some mild assumptions, we prove the global convergence of the algorithm on general manifolds and further establish the convergence rate and the iteration complexity bound of the algorithm. Experimental results indicate that, the proposed algorithm is highly competitive in terms of computational performance on specific problems and outperforms several existing algorithms.</p>

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A Riemannian Simulated Annealing-Based Barzilai–Borwein Gradient Method for Manifold Optimization

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Xue-Jie Wang,
  • Zheng Peng,
  • Xiao-Jiao Tong

摘要

We propose a novel Riemannian simulated annealing-based Barzilai–Borwein (RSABB) gradient method for optimization on manifolds. This hybrid approach combines the Barzilai–Borwein (BB) gradient method with a simulated annealing (SA) rule, tailored for optimization problems on the Stiefel manifold. The BB step size we utilize possesses a two-dimensional quadratic termination property. The proposed RSABB gradient method accepts the BB step according to SA rule, resulting in a new nonmonotone line search technique. If the BB step is not accepted, an Armijo line search is employed instead. Under some mild assumptions, we prove the global convergence of the algorithm on general manifolds and further establish the convergence rate and the iteration complexity bound of the algorithm. Experimental results indicate that, the proposed algorithm is highly competitive in terms of computational performance on specific problems and outperforms several existing algorithms.