Proximal quasi-Newton methods for nondifferentiable convex optimization

被引：0
|
作者：
Xiaojun Chen
Masao Fukushima
机构：
[1] Department of Mathematics and Computer Science,
[2] Shimane University,undefined
[3] Matsue 690-8504,undefined
[4] Japan,undefined
[5] e-mail: chen@math.shimane-u.ac.jp. Some of this work was supported by the Australian Research Council.,undefined
[6] Department of Applied Mathematics and Physics,undefined
[7] Graduate School of Informatics,undefined
[8] Kyoto University,undefined
[9] Kyoto 606-8501,undefined
[10] Japan,undefined
[11] e-mail: fuku@kuamp.kyoto-u.ac.jp. This author’s work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education,undefined
[12] Science and Culture,undefined
[13] Japan.,undefined
来源：
Mathematical Programming | 1999年 / 85卷
关键词：
Key words: nondifferentiable convex optimization – proximal point – quasi-Newton method – cutting-plane method – bundle methods Mathematics Subject Classification (1991): 65K05, 90C30;
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学科分类号：
摘要：
. 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 xk to 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.
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页码：313 / 334
页数：21
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