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Article overview
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Further properties of the forward-backward envelope with applications to difference-of-convex programming | Tianxiang Liu
; Ting Kei Pong
; | Date: |
1 May 2016 | Abstract: | In this paper, we further study the forward-backward envelope first
introduced in [27] and [29] for problems whose objective is the sum of a proper
closed convex function and a smooth 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-{L}ojasiewicz function with an exponent of $frac12$; 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 $ell_{1-2}$
regularized least squares problems [36] illustrate that an implementation of
this approach with a limited-memory BFGS scheme outperforms some standard
first-order methods such as the nonmonotone proximal gradient method in [34]. | Source: | arXiv, 1605.0201 | Services: | Forum | Review | PDF | Favorites |
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