Publication: Proximal gradient method with automatic selection of the parameter by automatic differentiation
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Proximal gradient method with automatic selection of the parameter by automatic differentiation

- Article in a journal -
 

Author(s)
Yingyi Li , Haibin Zhang , Zhibao Li , Huan Gao

Published in
Special issue of Optimization Methods & Software: Advances in Algorithmic Differentiation Optimization Methods & Software

Editor(s)
Bruce Christianson, Shaun A. Forth, Andreas Griewank

Year
2018

Publisher
Taylor & Francis

Abstract
A class of non-smooth convex optimization problems which arise naturally from applications in sparse group Lasso, have attracted significant research efforts for parameters selection. For given parameters of the problem, proximal gradient method (PGM) is effective to solve it with linear convergence rate and the closed form solution can be obtained at each iteration. However, in many practical applications, the selection of the parameters not only affects the quality of solution, but also even determines whether the solution is right or not. In this paper, we study a new method to analyse the impact of the parameters on PGM algorithm to solve the non-smooth convex optimization problem. We present the sensitivity analysis on the output of an optimization algorithm over parameter, and show the advantage of the technique using automatic differentiation. Then, we propose a hybrid algorithm for selecting the optimal parameter based on the method of PGM. The numerical results show that the proposed method is effective for the solving of sparse signal recovery problem.

Cross-References
Christianson2018Sio

BibTeX
@ARTICLE{
         Li2018Pgm,
       crossref = "Christianson2018Sio",
       author = "Yingyi Li and Haibin Zhang and Zhibao Li and Huan Gao",
       title = "Proximal gradient method with automatic selection of the parameter by automatic
         differentiation",
       journal = "Optimization Methods \& Software",
       volume = "33",
       number = "4--6",
       pages = "708--717",
       year = "2018",
       publisher = "Taylor \& Francis",
       doi = "10.1080/10556788.2018.1435648",
       url = "https://doi.org/10.1080/10556788.2018.1435648",
       eprint = "https://doi.org/10.1080/10556788.2018.1435648",
       abstract = "A class of non-smooth convex optimization problems which arise naturally from
         applications in sparse group Lasso, have attracted significant research efforts for parameters
         selection. For given parameters of the problem, proximal gradient method (PGM) is effective to solve
         it with linear convergence rate and the closed form solution can be obtained at each iteration.
         However, in many practical applications, the selection of the parameters not only affects the
         quality of solution, but also even determines whether the solution is right or not. In this paper,
         we study a new method to analyse the impact of the parameters on PGM algorithm to solve the
         non-smooth convex optimization problem. We present the sensitivity analysis on the output of an
         optimization algorithm over parameter, and show the advantage of the technique using automatic
         differentiation. Then, we propose a hybrid algorithm for selecting the optimal parameter based on
         the method of PGM. The numerical results show that the proposed method is effective for the solving
         of sparse signal recovery problem.",
       booktitle = "Special issue of Optimization Methods \& Software: Advances in
         Algorithmic Differentiation",
       editor = "Bruce Christianson and Shaun A. Forth and Andreas Griewank"
}


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