Study On The Global Convergence Of Some Hybrid Nonlinear Conjugate Gradient Algorithms

Since the conjugate gradient method has the advantages of simple design and small storage space, the conjugate gradient method is often used to deal with large-scale unconstrained optimization problems and monotone nonlinear equations with convex constraints. As is well known to us, the key to use the conjugate gradient method for solving problems is the construction of the conjugate parameter and the choice of step-size. Firstly, this paper constructs the conjugate parameter with sufficiently descent property. Secondly, with the aid of the conjugate parameter we proposed, this paper choose proper line search to ensure the global convergence of the new algorithm under appropriate hypotheses.1. For solving unconstrained optimization problems, this paper mainly proposed two different types of piece-wise DY conjugate gradient methods. The first kind of conjugate gradient method is that this paper is that a new non-negative and segmental conjugate parameter is constructed based on MDY method. The second kind of conjugate gradient method is that established on the MDY method with new parameters, we properly introduce CD method with the same parameter, and construct a new segmentation algorithm.2. For the first algorithm, the iterative structure used in this paper is commonly iterative structure, and this paper proves the global convergence of the algorithm by virtue of strong Wolfe line search. For the second algorithm, this paper abandons the traditional iterative structure, and employs the new iterative structure proposed by Li and Fukushima[12]. Finally, this paper proves the global convergence properties of the algorithm with the new iterative structure under the strong Wolfe line search condition. At the same time, preliminary numerical experiments shows that the two algorithms are efficient and robust.