Research On Nonlinear Conjugate Gradient Method With Several Parameters

Conjugate gradient method enjoys a long history of more than 51 years and has been the focus of the research on the optimization algorithm. It has been widely used to solve theoretical and practical problems duo to its benefits in memory saving, global convergence and ease of implementation. In this paper we first give a brief introduction of the research condition, then present a novel method, prove the property of global convergence and sufficient descent, finally show the numerical experiments and the results. Our paper including four sections.In the first section, we introduce the foundational knowledge, development of conjugate gradient method, line search condition, the assumption on objective function, the important lemma and the main results obtain in this paper.In the second section, we propose a new spectral conjugate gradient method which is global convergence under the strong Wolfe line search conditions and satisfies the sufficient descent condition 2kk T kgcdg ?? under the any line search condition. It has inherent property when?0k?. We compare the new method with the FR method, and CD method under the strong Wolfe line search condition, Numerical experiments show that the new method is very efficient.In the third section, we propose a hybrid spectral conjugate gradient method which is global convergence and satisfies the sufficient descent condition2 kk T kgcdg ?? under the any line search. We compare the new method with the FR method, CD method, DY method and SP method under the strong Wolfe line search condition, Numerical experiments show that the new method is very efficient.In the fourth section, we propose a new conjugate gradient method which is global convergence and satisfies the sufficient descent condition 2kk T kgcdg ?? under the strong Wolfe line search conditions. We compare the new method with the FR method, CD method, and WEI method under the strong Wolfe line search condition, Numerical experiments show that the new method is efficient.In the fifth section, we proposed a new modified HH method in the fourth section. Compare with the HH method and the WEI method which show that the new method is efficient.