A modified Liu-Storey-Conjugate descent hybrid projection method for convex constrained nonlinear equations and image restoration

<p style='text-indent:20px;'>We present an iterative method for solving the convex constraint nonlinear equation problem. The incorporates projection strategy by Solodov and Svaiter with hybrid Liu-Storey Conjugate descent Yang et al. unconstrained optimization proposed does not require Jacobian information, nor it to store any matrix at each iteration. Thus, has potential solve large-scale non-smooth problems. Under some standard assumptions, convergence analysis of is established. Finally, show applicability method, used <inline-formula><tex-math id="M1">\begin{document}$ \ell_1 $\end{document}</tex-math></inline-formula>-norm regularized problems restore blurred noisy images. numerical experiment indicates that our result a significant improvement compared related methods problem.</p>