A Descent Conjugate Gradient Algorithm for Optimization Problems and Its Applications in Image Restoration and Compression Sensing

Abstract

It is well known that the nonlinear conjugate gradient algorithm is one of the effective algorithms for optimization problems since it has low storage and simple structure properties. This motivates us to make a further study to design a modified conjugate gradient formula for the optimization model, and this proposed conjugate gradient algorithm possesses several properties: (1) the search direction possesses not only the gradient value but also the function value; (2) the presented direction has both the sufficient descent property and the trust region feature; (3) the proposed algorithm has the global convergence for nonconvex functions; (4) the experiment is done for the image restoration problems and compression sensing to prove the performance of the new algorithm.