1. A Bregman proximal subgradient algorithm for nonconvex and nonsmooth fractional optimization problems.
- Author
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Long, Xian Jun, Wang, Xiao Ting, Li, Gao Xi, and Li, Geng Hua
- Subjects
- *
NONSMOOTH optimization , *SMOOTHNESS of functions , *ALGORITHMS , *CONVEX functions - Abstract
In this paper, we study a class of nonconvex and nonsmooth fractional optimization problem, where the numerator of which is the sum of a nonsmooth and nonconvex function and a relative smooth nonconvex function, while the denominator is relative weakly convex nonsmooth function. We propose a Bregman proximal subgradient algorithm for solving this type of fractional optimization problems. Under moderate conditions, we prove that the subsequence generated by the proposed algorithm converges to a critical point, and the generated sequence globally converges to a critical point when the objective function satisfies the Kurdyka-Łojasiewicz property. We also obtain the convergence rate of the proposed algorithm. Finally, two numerical experiments illustrate the effectiveness and superiority of the algorithm. Our results give a positive answer to an open problem proposed by Bot et al. [14]. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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