Proximal quasi-Newton methods for nondifferentiable convex optimization
Proximal quasi-Newton methods for nondifferentiable convex optimization
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DOI：
10.1007/s101070050059
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发表时间：
1999-06
影响因子：
2.7
通讯作者：
Xiaojun Chen;M. Fukushima
中科院分区：
文献类型：
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作者：
Xiaojun Chen;M. Fukushima
名词该方法基于 Rockafellar 的近点算法和剖切面技术。在每一步中，我们使用xk的近似近点pa(xk)来定义vk∈∂εkf(pa(xk))，其中εk≤α∥vk∥，其中α是常数。该方法监视∥vk∥值的减少，以识别何时应使用f上的线搜索。使用拟牛顿步来减小∥vk∥的值。在 f 不存在可微性的情况下，该方法全局收敛，收敛速度为 Q 线性。还讨论了超线性收敛以扩展 Dennis 和 Moree 的表征结果。数值结果表明该方法具有良好的性能。
n. The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point pa(xk) of xkto define a vk∈∂εkf(pa(xk)) with εk≤α∥vk∥, where α is a constant. The method monitors the reduction in the value of ∥vk∥ to identify when a line search on f should be used. The quasi-Newton step is used to reduce the value of ∥vk∥. Without the differentiability of f, the method converges globally and the rate of convergence is Q-linear. Superlinear convergence is also discussed to extend the characterization result of Dennis and Moré. Numerical results show the good performance of the method.