一类具有自适应重启策略的混合黎曼共轭梯度算法
A Family of Hybrid Riemannian Conjugate Gradient Algorithms with an Adaptive Restart Strategy
摘要: 本文针对黎曼流形上的非凸优化问题，提出了一类具有自适应重启策略的混合型黎曼共轭梯度算 法。该算法能够在不依赖于特定步长策略的情况下，在黎曼流形上生成有效的下降方向。在满足 常见假设的基础下，结合黎曼弱 Wolfe 线搜索条件，我们进一步证明了算法的全局收敛性。最 后，通过数值实验验证了所提方法在测试问题中的有效性，与现有的黎曼共轭梯度方法相比，表 现出更优的性能。
Abstract: In this work, we propose a class of hybrid Riemannian conjugate gradient algorithm- s with an adaptive restart strategy for solving nonconvex optimization problems on Riemannian manifolds. The proposed method is capable of generating effective de- scent directions on manifolds without relying on specific stepsize strategies. Under standard assumptions and in conjunction with the Riemannian weak Wolfe line search conditions, we establish the global convergence of the algorithm. Numerical experi- ments on benchmark problems demonstrate the efficiency of the proposed method and show that it outperforms existing Riemannian conjugate gradient methods in terms of practical performance.
文章引用：郭雨欣, 肖艳阳, 朱俊杰. 一类具有自适应重启策略的混合黎曼共轭梯度算法[J]. 应用数学进展, 2025, 14(9): 22-34. https://doi.org/10.12677/AAM.2025.149396

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