随机初级-双元混合梯度算法与自适应式步骤大小
Antonin Chambolle1,2, Claire Delplancke3, Matthias J Ehrhardt4
1CEREMADE, Université Paris-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775 Paris, France.
概括
本研究介绍了随机初级-双元混合梯度 (SPDHG) 算法的适应性步骤大小,改进了大规模的凸式优化. 新的自适应式SPDHG (A-SPDHG) 确保了融合,并为增强性能提供了实用的参数选择.
科学领域:
- 优化算法 优化算法
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
背景情况:
- 随机原始-双重混合梯度 (SPDHG) 算法由于其可扩展性,被广泛用于大规模的凸式优化.
- SPDHG的收依赖于初级和双级尺寸的产品的上限.
- 在实际应用中,为SPDHG选择最佳的步骤尺寸比仍然是一个挑战.
研究的目的:
- 为凸优化开发一种具有适应性步骤大小的新型原始-双元算法.
- 介绍一个适应式SPDHG (A-SPDHG) 算法的一般类别.
- 提供系统的策略来选择SPDHG中的步骤大小,以确保融合.
主要方法:
- 提出了一个适应性SPDHG (A-SPDHG) 算法的一般类.
- 在弱假设下证明了A-SPDHG的收性质.
- 为A-SPDHG制定了具体的参数更新策略.
主要成果:
- 证明了拟议的A-SPDHG算法的融合.
- 通过数值示例验证了适应性方案的有效性.
- 展示了计算机断层扫描重建中的成功应用.
结论:
- 针对SPDHG算法的拟议的自适应步骤大小策略增强了趋同性和实际适用性.
- A-SPDHG为大规模的凸式优化问题提供了强大的解决方案.
- 开发的方法为步骤大小选择提供了一个系统的方法,克服了以前的局限性.
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