On The Research Of Optimization Methods And Supply Chain Information Management

Among the quasi-Newton methods for solving unconstrained optimization problems in numerical result, the BFGS algorithm constitutes a particularly important class. This method converges globally and locally very well.Because of the density of the matrices produced by the BFGS method generally, it must adopt particular sparse technique for solving large dimensional optimization problems. Toint (1981) proposed a partially separable BFGS method for solving convex partially separable minimization. Thereby, the Hessian matrix of the objective function being similar to a block diagonal sparse matrix is maintained by the updated matrix sequence. Toint (1982) obtained local convergence of the partially separable BFGS method when the elemental objective functions are convex. Moreover, Toint (1986) obtained global convergence of this method with Wolfe-Powell line search.We propose a modification of the BFGS method based on the modified BFGS (MBFGS) formula given by Li-Fukushima (2001) for solving nonconvex partially separable minimization. It's one of the main achievements of this paper. In the method, the symmetric positive semidefinite matrices are updated to approximate the Hessian matrices of the elemental objective functions and their sum to approximate the Hessian matrix of the objective function. Thereby, sparsity of the Hessian matrix of the objective function is maintained by the approximate updated matrix sequence. Moreover, the updated matrix sequence is a symmetric positive definite matrix sequence. Under some weak conditions, the global convergence theorem of the method is established. The result may be regarded as an extension of the partitioned BFGS algorithm proposed by Toint (1986).The other we study in this paper is logistics and supply chain management. The new and old model of EDI, direct EDI using for special purpose, EDI based on VAN, and EDI based on Internet (Internet Mail, Standard IC, Wed-EDI, XML/EDI) are compared in detail, further studied and extensively explored. Furthermore, the domestic and international development situation and perspectives of EDI is analyzed systematically.The structural changes from E-commerce to M-commerce and its profound influence are analyzed systematically. We further study M-commerce as the new opportunity of 21 century global development: the primary impetus of new economy, the key reason of accelerating economy globally, the key content of pushing trade globally, and the effective means of speeding up finance globally in detail. Then we explore technology, service and environ-...