TWO MODIFIED CONJUGATE GRADIENT METHODS AND THEIR APPLICATION TO IMAGE RESTORATION PROBLEMS

Conjugate gradient methods have significantly contributed to the discovery of minimizes of large-scale unconstrained optimization problems. In this paper, based on the Liu--Storey conjugate gradient method, two modified conjugate gradient methods (named MC1 and MC2 methods) are presented for unconstrained optimization. Under usual assumptions, the two presented methods are proven to be sufficient descent at each iteration. The global convergence results of our methods is established using the strong Wolfe line search (SWLS). Numerical tests demonstrate the effectiveness of the MC1 and MC2 methods when compared to certain existing methods in view of the Dolan and Moré performance profile. Furthermore, the practica applications of these methods in image restoration problems is also considered.