tailieunhanh - Báo cáo hóa học: " Modified nonlinear conjugate gradient method with sufficient descent condition for unconstrained optimization"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Modified nonlinear conjugate gradient method with sufficient descent condition for unconstrained optimization | Liu and Wang Journal of Inequalities and Applications 2011 2011 57 http content 2011 1 57 3 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Modified nonlinear conjugate gradient method with sufficient descent condition for unconstrained optimization Jinkui Liu and Shaoheng Wang Correspondence liujinkui2006@ School of Mathematics and Statistics Chongqing Three Gorges University Chongqing Wanzhou People s Republic of China Springer Abstract In this paper an efficient modified nonlinear conjugate gradient method for solving unconstrained optimization problems is proposed. An attractive property of the modified method is that the generated direction in each step is always descending without any line search. The global convergence result of the modified method is established under the general Wolfe line search condition. Numerical results show that the modified method is efficient and stationary by comparing with the well-known Polak-Ribiére-Polyak method CG-DESCENT method and DSP-CG method using the unconstrained optimization problems from More and Garbow ACM Trans Math Softw 7 17-41 1981 so it can be widely used in scientific computation. Mathematics Subject Classification 2010 90C26 65H10 1 Introduction The conjugate gradient method comprises a class of unconstrained optimization algorithms which is characterized by low memory requirements and strong local or global convergence properties. The purpose of this paper is to study the global convergence properties and practical computational performance of a modified nonlinear conjugate gradient method for unconstrained optimization without restarts and with appropriate conditions. In this paper we consider the unconstrained optimization problem min f x x e Rn where f Rn R is a real-valued continuously differentiable function. When applied to the nonlinear problem a nonlinear conjugate gradient method generates a sequence xk