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We propose an effective conjugate gradient method belonging to the class of Dai–Liao methods for solving unconstrained optimization problems. We employ a variant of the modified secant condition and introduce a new conjugate gradient parameter by solving an optimization problem. The optimization problem combines the well-known features of the linear conjugate gradient method using some penalty functions. This new parameter takes advantage of function information as well as the gradient information to provide the iterations. Our proposed method is globally convergent under mild assumptions. We examine the ability of the method for solving some real-world problems from image processing field. Numerical results show that the proposed method is efficient in the sense of the PSNR test. We also compare our proposed method with some well-known existing algorithms using a collection of CUTEr problems to show its efficiency.

A new conjugate gradient method based on a modified secant condition with its applications in image processing