A Kind Of Improvement Of Conjugate Gradient Method

Conjugate gradient method has the advantages of small storage required,simple iteration format,and the iterative process can be completed by using only the objective function value and its gradient value.It has been widely used in the engineering field and is especially suitable for solving large-scale unconstrained optimization problems.Therefore,improving the conjugate gradient method has always been one of the hot spots in the field of optimization.It is the goal pursued by many researchers to improve the computational efficiency of the algorithm while ensuring the convergence.Proposing a conjugate gradient algorithm with good convergence and good numerical performance has important theoretical significance and practical value.In this paper,we study three conjugate gradient methods,which are divided into two parts.In the first part,inspired by the three-term PRP conjugate gradient method studied by the predecessors,the general framework of the first type of three-term conjugate gradient method is given.The third term can be any given vector.By adjusting the coefficients and negative gradient coefficients,the direction generated is guaranteed to have sufficient descending properties.The value of the coefficients in this article is within an interval.And under appropriate assumptions,a proof of the global convergence of the algorithm under Armijo criterion and back-off method is given.The test results of20 calculation examples are given at the end of Chapter 2,which shows that the new algorithm has good numerical performance.The second part gives the general framework of the three-term FR conjugate gradient method.Similar to the first part,the third term given is still any given vector.By adjusting the coefficient and the coefficient of the negative gradient,it is ensured that the direction generated has a sufficient decline,and the value of the coefficient is still within an interval.And under appropriate assumptions,the proof of the global convergence of the method under the Armijo criterion and the backward method is given.The test results of 24 calculation examples are given at the end of Chapter 3,which shows that the new algorithm has good numerical performance.