Abstract
In this paper, based on the inertial acceleration technique, we propose a family of inertial derivative-free projection methods for solving nonlinear pseudo-monotone equations with convex constraints, in which the search direction is only required to satisfy the sufficient descent condition. The global convergence of the family is established without the Lipschitz continuity of the underlying mapping. To the best of our knowledge, this is the first convergence result for inertial-type algorithms in the pseudo-monotone scenario, and it is also very few for the monotone scenario in the literature since the well-established condition to ensure convergence in this scenario is replaced with a weaker one. Moreover, we propose an inertial derivative-free projection method by embedding a specific search direction into the family. Our numerical experiments on the standard constrained nonlinear equations illustrate the effectiveness and efficiency of the proposed method compared with two state-of-the-art methods. Finally, applying it to solve the regularized decentralized logistic regression shows that our method is quite promising.
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Notes
All codes are available at https://github.com/jhyin-optim/FIDFPMs_MATLABcodes.
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This work was supported by the National Natural Science Foundation of China (12171106) and the Natural Science Foundation of Guangxi Province (2020GXNSFDA238017).
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Jian, J., Yin, J., Tang, C. et al. A family of inertial derivative-free projection methods for constrained nonlinear pseudo-monotone equations with applications. Comp. Appl. Math. 41, 309 (2022). https://doi.org/10.1007/s40314-022-02019-6
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DOI: https://doi.org/10.1007/s40314-022-02019-6
Keywords
- Nonlinear pseudo-monotone equations
- Derivative-free projection method
- Inertial acceleration technique
- Convergence