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Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing

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Abstract

In this paper, we present two new three-term conjugate gradient methods which can generate sufficient descent directions for the large-scale optimization problems. Note that this property is independent of the line search used. We prove that these three-term conjugate gradient methods are global convergence under the Wolfe line search. Numerical experiments and comparisons demonstrate that the proposed algorithms are efficient approaches for test functions. Moreover, we use the proposed methods to solve the \(\ell _1-\alpha \ell _2\) regularization problem of sparse signal decoding in compressed sensing, and the results show that our methods have certain advantages over the existing solvers on such problems.

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Authors and Affiliations

  1. School of Electronic Engineering and Automation, Guangxi Key Laboratory of Automatic Detecting Technology and Instruments, Guilin University of Electronic Technology, Guilin, 541004, China

    Yufeng Liu & Benxin Zhang

  2. School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, 541004, China

    Zhibin Zhu

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  1. Yufeng Liu
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  2. Zhibin Zhu
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Correspondence to Zhibin Zhu.

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This work is supported by the National Natural Science Foundation of China (61967004, 11901137, 11961011), Guangxi Natural Science Foundation (2018GXNSFBA281023), China Postdoctoral Science Foundation (2020M682959), Guangxi Key Laboratory of Cryptography and Information Security (GCIS201927), Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20113) , and Innovation Project of Guangxi Graduate Education (2021YCXS118)

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Liu, Y., Zhu, Z. & Zhang, B. Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing. J. Appl. Math. Comput. 68, 1787–1816 (2022). https://doi.org/10.1007/s12190-021-01589-8

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