University of Guilan Journal of Mathematical Modeling 2345-394X 12 2 2024 07 01 A hybrid CG algorithm for nonlinear unconstrained optimization with application in image restoration 301 317 7567 10.22124/jmm.2024.26151.2317 EN Choubeila Souli Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria Raouf Ziadi Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria Abdelatif Bencherif-Madani Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria Hisham Mohammed Khudhur Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq Journal Article 2023 11 28 This paper presents a new hybrid conjugate gradient method for solving  nonlinear unconstrained optimization problems; it is based on a combination of $RMIL$  (Rivaie-Mustafa-Ismail-Leong)  and $hSM$  (hybrid Sulaiman- Mohammed) methods. The proposed algorithm enjoys the sufficient descent condition without depending on any line search; moreover, it is globally convergent under the usual and strong Wolfe line search assumptions.  The performance of the algorithm is demonstrated through numerical experiments on a set of 100 test functions from [1] and four image restoration problems with two noise levels. The numerical comparisons with four existing methods show that the proposed method is promising and effective. https://jmm.guilan.ac.ir/article_7567_a6b0819e4c4f3837f68f8ebd7e94dc47.pdf