A new conjugate gradient projection method for convex constrained nonlinear equations.

*(English)*Zbl 1444.65022Summary: The conjugate gradient projection method is one of the most effective methods for solving large-scale monotone nonlinear equations with convex constraints. In this paper, a new conjugate parameter is designed to generate the search direction, and an adaptive line search strategy is improved to yield the step size, and then, a new conjugate gradient projection method is proposed for large-scale monotone nonlinear equations with convex constraints. Under mild conditions, the proposed method is proved to be globally convergent. A large number of numerical experiments for the presented method and its comparisons are executed, which indicates that the presented method is very promising. Finally, the proposed method is applied to deal with the recovery of sparse signals.

##### MSC:

65H10 | Numerical computation of solutions to systems of equations |

65K05 | Numerical mathematical programming methods |

##### Software:

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\textit{P. Liu} et al., Complexity 2020, Article ID 8323865, 14 p. (2020; Zbl 1444.65022)

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