Convergence analysis of a proximal-type algorithm for DC programs with applications to variable selection
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866908874488938496 |
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| author | Wu, Shuang Van Dinh, Bui Jiao, Liguo Kim, Do Sang Zhu, Wensheng |
| author_facet | Wu, Shuang Van Dinh, Bui Jiao, Liguo Kim, Do Sang Zhu, Wensheng |
| contents | We consider a minimization problem of the form $P(φ, g, h):$ $$\min\left\{f(x):= φ(x) + g(x) - h(x) \colon x \in \mathbb{R}^n\right\},$$ where $φ$ is a differentiable function and $g,$ $h$ are convex functions, and introduce iterative methods to finding a critical point of $f$ when $f$ is differentiable. We show that the point computed by proximal point algorithm at each iteration can be used to determine a descent direction for the objective function at this point. This algorithm can be considered as a combination of proximal point algorithm together with a linesearch step that uses this descent direction. We also study convergence results of these algorithms and the inertial proximal methods proposed by Maing$\acute{e}$ and Moudafi (SIAM J. Optim. {\bf 19}(2008), 397--413) under the main assumption that the objective function satisfies the Kurdika--Łojasiewicz property. The proposed algorithm is then applied to solve the variable selection problem in linear regression. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1508_03899 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of a proximal-type algorithm for DC programs with applications to variable selection Wu, Shuang Van Dinh, Bui Jiao, Liguo Kim, Do Sang Zhu, Wensheng Optimization and Control 49J52, 49J53, 65K10, 49M37 We consider a minimization problem of the form $P(φ, g, h):$ $$\min\left\{f(x):= φ(x) + g(x) - h(x) \colon x \in \mathbb{R}^n\right\},$$ where $φ$ is a differentiable function and $g,$ $h$ are convex functions, and introduce iterative methods to finding a critical point of $f$ when $f$ is differentiable. We show that the point computed by proximal point algorithm at each iteration can be used to determine a descent direction for the objective function at this point. This algorithm can be considered as a combination of proximal point algorithm together with a linesearch step that uses this descent direction. We also study convergence results of these algorithms and the inertial proximal methods proposed by Maing$\acute{e}$ and Moudafi (SIAM J. Optim. {\bf 19}(2008), 397--413) under the main assumption that the objective function satisfies the Kurdika--Łojasiewicz property. The proposed algorithm is then applied to solve the variable selection problem in linear regression. |
| title | Convergence analysis of a proximal-type algorithm for DC programs with applications to variable selection |
| topic | Optimization and Control 49J52, 49J53, 65K10, 49M37 |
| url | https://arxiv.org/abs/1508.03899 |