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Volume 2, Issue 4
A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

Zheng-Jian Bai, Michael K. Ng & Liqun Qi

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 377-402.

Published online: 2009-02

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  • Abstract

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.

  • AMS Subject Headings

65F22, 65K05

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COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-377, author = {Zheng-Jian Bai, Michael K. Ng and Liqun Qi}, title = {A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {4}, pages = {377--402}, abstract = {

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2009.m9002s}, url = {http://global-sci.org/intro/article_detail/nmtma/6030.html} }
TY - JOUR T1 - A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization AU - Zheng-Jian Bai, Michael K. Ng & Liqun Qi JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 377 EP - 402 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/10.4208/nmtma.2009.m9002s UR - https://global-sci.org/intro/article_detail/nmtma/6030.html KW - Coordinate descent, global convergence, linear convergence rate. AB -

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.

Zheng-Jian Bai, Michael K. Ng and Liqun Qi. (2009). A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization. Numerical Mathematics: Theory, Methods and Applications. 2 (4). 377-402. doi:10.4208/nmtma.2009.m9002s
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