Some Researches On Nonlinear Conjugate Gradient Method For Unconstrained Optimization Problem

In this master’s thesis, we mainly discuss the descent property and global con-vergence of conjugate gradient method for unconstrained optimization problems. This thesis is divided into four parts.In Chapter One, a brief introduction to the development and research actuality of nonlinear conjugate gradient method is presented, the importance of conjugate gradient method is emphasised, some famous line search technology and classical conjugate gradient methods are listed. At last, we introduce the arrangement for the contents.In Chapter Two, inspired by the literature [27], we construct a new βk*by introducing a parameter θ, then a new conjugate gradient method is constructed with the Armijo line search technology. The sufficient descent property of the modified PRP conjugate gradient method is firstly proved. Secondly, we establish the global convergence of the method. Numerical results indicate the algorithm is effective in the end.In Chapter Three, based on the new βk*in Chapter Two, with the Armijo line search technology, a new conjugate gradient method is constructed by introducing a new search direction dk.We firstly prove the sufficient descent property of the method. Secondly, we establish the global convergence of the method. Numerical results indicate the algorithm is effective in the end.In Chapter Four, the research is summarized. We also discuss the ideas, expec-tation, suggestions and unsolved problems of the research in the future.