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Two spectral conjugate gradient methods for unconstrained optimization problems

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Abstract

Two new spectral conjugate gradient methods (ZL1 method and ZL2 method) for solving unconstrained optimization problems are established. Under the standard Wolfe line search, the search direction generated by the ZL1 method is a descent direction. The search direction of the ZL2 method satisfies descent property independent of the line search. The global convergence of the two new methods can be demonstrated under the standard Wolfe line search. Numerical experiments are presented to show that the two methods are effective.

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Authors and Affiliations

  1. 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, Ai Long & Tian Wang

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  1. Zhibin Zhu
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  2. Ai Long
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  3. Tian Wang
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Correspondence to Ai Long.

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This work is supported by the National Natural Science Foundation of China (61967004, 11901137), Guangxi Key Laboratory of Cryptography and Information Security (GCIS201927, GCIS201621) and Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (YQ20113, YQ20114)

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Zhu, Z., Long, A. & Wang, T. Two spectral conjugate gradient methods for unconstrained optimization problems. J. Appl. Math. Comput. 68, 4821–4841 (2022). https://doi.org/10.1007/s12190-022-01730-1

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  • DOI: https://doi.org/10.1007/s12190-022-01730-1

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