Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1886-1897.

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Spectral LS-type Projection Algorithm for Solving Nonlinear Pseudo-Monotone Equations

Ning Zhang(),Jinkui Liu*()   

  1. School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100
  • Received:2022-03-22 Online:2022-12-26 Published:2022-12-16
  • Contact: Jinkui Liu;
  • Supported by:
    the Chongqing Research Program of Basic Research and Frontier Technology(cstc2021jcyj-msxmX0233);the Chongqing Three Gorges University Graduate Research Innovation Project(YJSKY22058)


Based on the structures of the spectral gradient method and the famous LS conjugate gradient method, in this paper we establish an spectral LS-type derivative-free projection algorithm to solve nonlinear pseudo-monotone equations with convex constraints. By using the spectral parameter, the proposed method can generate the descent direction in each iterate, which is independent of any line search. Under some usual assumptions, the global convergence of the proposed method is proved by using the classical derivative-free line search condition. Numerical experiments show that the proposed method inherits the excellent computational performance of the LS conjugate gradient method and improves its stability.

Key words: Nonlinear equations, Derivative-free projection method, Derivative-free line search, Global convergence

CLC Number: 

  • O241