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

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. 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 PSNR test. We also compare our proposed method with some well-known existing algorithms using a collection of CUTEr problems to show it's efficiency.

A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

A Descent Dai-Liao Conjugate Gradient Method Based on a Modified Secant Equation and Its Global Convergence

We propose a conjugate gradient method which is based on the study of the Dai-Liao conjugate gradient method. An important property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. Moreover, it achieves a high-order accuracy in approximating the second-order curvature information of the objective function by utilizing the modified secant condition proposed by Babaie-Kafaki et al. (2010). Under mild conditions, we establish that the proposed method is globally convergent for general functions provided that the line search satisfies the Wolfe conditions. Numerical experiments are also presented.