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Difference-of-Convex Algorithm with Extrapolation for Nonconvex, Nonsmooth Optimization Problems.
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- Author(s): Phan, Duy Nhat; Le Thi, Hoai An
- Source:
Mathematics of Operations Research; Aug2024, Vol. 49 Issue 3, p1973-1985, 13p- Subject Terms:
- Source:
- Additional Information
- Abstract: In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration technique and the DC algorithm to develop a novel algorithm for the considered problem. We then study the subsequential convergence of our algorithm to a critical point. Furthermore, we justify the global convergence of the whole sequence generated by our algorithm to a critical point and establish its convergence rate under the Kurdyka–Łojasiewicz condition. Numerical experiments on the nonnegative matrix completion problem are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods. [ABSTRACT FROM AUTHOR]
- Abstract: Copyright of Mathematics of Operations Research is the property of INFORMS: Institute for Operations Research and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Abstract:
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