A numerical solution of the elasticity problem of settled of the wronkler ground with variable coefficients

In this paper, we have given numerical solution of the elasticity problem of settled on the wronkler ground with variable coefficient. The approximation solution of boundary value problem which is pertinent to this has been converted to integral equations, and then by using the successive approximation methods, has been reached. In addition to this, the approximation solution of the problem was put into Padé series form. We applied these methods to an example which is the elasticity problem of unit length homogeny beam, which is a special form of boundary value problem. First we calculate the successive approximation of the given boundary value problem then transform it into Padé series form, which give an arbitrary order for solving differential equation numerically.     

Pairwise reactive sor algorithm for quadratic programming of net import spatial equilibrium models

An iterative method based on the successive overrelaxation (SOR) is proposed to solve quadratic programming of net important spatial equilibrium models. The algorithm solves the problem by updating the variables pairwise at each iteration. The principal feature of the algorithm is that the lagrange multipliers corresponding to the constraints do not have to be calculated at each iteration as is the case in SOR based algorithms. Yet the Lagrange multipliers can easily be extracted from the solution values.This research was partially supported by grants from the James F. Kember Foundation and the School of Business, Loyola University of Chicago.     

关于调整气象观测站问题的数学模型

本文讨论了西安市第一届大学生数学模型竞赛题之一——调整气象观测站问题．若用主成份与逐步剔除法解决此问题，似可根据“损失信息量”的概念来确定减少测站个数．通过计算分析，在不损失信息量的条件下，可以去掉两个测站；在损失信息量为０．８５２％的条件下，可以去掉３个测站．这种算法，使节约设站开资，减少测站数量更具科学性．     

Extended Hartree-Fock (EHF) theory of chemical reactions

The triplet-instability analysis of the closed-shell RHF solutions has been carried out in relation to the orbital and spin correlation effects for various transition structures (TS) and reaction intermediates. It is found that the RHF solutions even for cyclic transition states of the Woodward-Hoffmann symmetry-allowed reactions often involve the triplet instability, indicating the crucial role of correlation corrections. The di- and tetra-radical characters for the transition structures are calculated by the projected UHF (PUHF) solutions resulting from the instability. The spin projection is also crucial for the UHF Møller-Plesset (UMP) correlated wavefunctions obtained for the transition structures of 1,3-dipolar, Diels-Alder, ene and related reactions. The relative stability between cyclic and acyclic TS for these reactions is examined at the approximately projected UHF MP2 (APU MP2) level. The former is found to be more favorable than the latter if the correlation correction is taken into account for TS in a well-balanced manner.Dedicated to Professor J. Koutecký on the occassion of his 65th birthday     

On the problem of directed signal transmission and energy transfer in molecular systems

A new physical interpretation of the mechanism of directed energy transfer and signal transmission in molecular systems along one-dimensional chains capable of successive isomerization is proposed. The photoacceptor—transmitting chain—reaction center system is considered as a model. Conditions under which the directed energy transfer occurs from the photoacceptor to the reaction center along the chain are analyzed. The time of signal transmission depends on the chain length, and the transmission coefficient is mainly determined by the characteristics of the initial and final elements in the whole system.     

A successive quadratic programming method for a class of constrained nonsmooth optimization problems

In this paper we present an algorithm for solving nonlinear programming problems where the objective function contains a possibly nonsmooth convex term. The algorithm successively solves direction finding subproblems which are quadratic programming problems constructed by exploiting the special feature of the objective function. An exact penalty function is used to determine a step-size, once a search direction thus obtained is judged to yield a sufficient reduction in the penalty function value. The penalty parameter is adjusted to a suitable value automatically. Under appropriate assumptions, the algorithm is shown to produce an approximate optimal solution to the problem with any desirable accuracy in a finite number of iterations.     

求解界约束优化问题的有效集算法综述

主要介绍了求解界约束优化问题的有效集方法,包括投影共轭梯度法和有效集识别函数法,讨论了各自的优点和不足.最后,指出了有效集法的研究趋势及应用前景.     

A projected gradient method with nonmonotonic backtracking technique for solving convex constrained monotone variational inequality problem

Based on a differentiable merit function proposed by Taji, et al in “Mathematical Programming, 1993, 58： 369-383”, a projected gradient trust region method for the monotone variational inequality problem with convex constraints is presented. Theoretical analysis is given which proves that the proposed algorithm is globally convergent and has a local quadratic convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming

In this paper we establish the existence,uniqueness and iterative approximation of solutions fortwo classes of functional equations arising in dynamic programming of multistage decision processes.The resultspresented here extend,and unify the corresponding results due to Bellman,Bhakta and Choudhury,Bhaktaand Mitra,Liu and others.     

On filter-successive linearization methods for nonlinear semidefinite programming

In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.