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http://hdl.handle.net/10397/76268
| Title: | Further properties of the forward-backward envelope with applications to difference-of-convex programming | Authors: | Liu, TX Pong, TK |
Issue Date: | Jul-2017 | Source: | Computational optimization and applications, July 2017, v. 67, no. 3, p. 489-520 | Abstract: | In this paper, we further study the forward-backward envelope first introduced in Patrinos and Bemporad (Proceedings of the IEEE Conference on Decision and Control, pp 2358-2363, 2013) and Stella et al. (Comput Optim Appl, doi:10.1007/s10589-017-9912-y, 2017) for problems whose objective is the sum of a proper closed convex function and a twice continuously differentiable possibly nonconvex function with Lipschitz continuous gradient. We derive sufficient conditions on the original problem for the corresponding forward-backward envelope to be a level-bounded and Kurdyka-Aojasiewicz function with an exponent of ; these results are important for the efficient minimization of the forward-backward envelope by classical optimization algorithms. In addition, we demonstrate how to minimize some difference-of-convex regularized least squares problems by minimizing a suitably constructed forward-backward envelope. Our preliminary numerical results on randomly generated instances of large-scale regularized least squares problems (Yin et al. in SIAM J Sci Comput 37:A536-A563, 2015) illustrate that an implementation of this approach with a limited-memory BFGS scheme usually outperforms standard first-order methods such as the nonmonotone proximal gradient method in Wright et al. (IEEE Trans Signal Process 57:2479-2493, 2009). | Keywords: | Forward-backward envelope Kurdyka-Lojasiewicz property Difference-of-convex programming |
Publisher: | Springer | Journal: | Computational optimization and applications | ISSN: | 0926-6003 | EISSN: | 1573-2894 | DOI: | 10.1007/s10589-017-9900-2 | Rights: | © Springer Science+Business Media New York 2017 This is a post-peer-review, pre-copyedit version of an article published in Computational Optimization and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10589-017-9900-2 |
| Appears in Collections: | Journal/Magazine Article |
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| a0585-n01_FBE_nonconvex_re3.pdf | Pre-Published version | 1.14 MB | Adobe PDF | View/Open |
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