A hybrid CG algorithm for nonlinear unconstrained optimization with application in image restoration

Document Type : Research Article


1 Laboratory of Fundamental and Numerical Mathematics (LMFN), University Ferhat Abbas Setif 1, Algeria

2 Department of Mathematics, College of Computer Science and Mathematics, University of Mosul, Mosul, Iraq


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.


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