On the General Taylor Theorem and its Applications in Solving Non-lin-ear Problems

ＯｎｔｈｅＧｅｎｅｒａｌＴａｙｌｏｒＴｈｅｏｒｅｍａｎｄｉｔｓＡｐｐｌｉｃａｔｉｏｎｓｉｎＳｏｌｖｉｎｇＮｏｎｌｉｎｅａｒＰｒｏｂｌｅｍｓ１１ＴｈｅｐａｐｅｒｗａｓｒｅｃｅｉｖｅｄｏｎＪｕｌｙ．２０，１９９７ＳｈｉＪｕｎＬＩＡＯ（Ｄｅｐａｒｔｍｅ...     

The Property of Curve Triangle Number Table and Its Application

ＴｈｅＰｒｏｐｅｒｔｙｏｆＣｕｒｖｅＴｒｉａｎｇｌｅＮｕｍｂｅｒＴａｂｌｅａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎ￥ＨｕａｎｇＴｉａｎｍｉｎ；ＨｅＹｉｎｏｎｇ（Ｓｏｕｔｈｗｅｓｔ－ＪｉａｏｔｏｎｇＵｎｉｖｅｒｓｉｔｙ）（ＮａｎｙａｎｇＴｅａｃｈｅｒ＇ｓＣｏ...     

AHybridHighAccuracyDifferenceSchemeandItsApplications￣(1,2)

ＡＨｙｂｒｉｄＨｉｇｈＡｃｃｕｒａｃｙＤｉｆｆｅｒｅｎｃｅＳｃｈｅｍｅａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎｓ￣（１，２）ＲｕｑｕａｎＷＡＮＧ，ＷｅｉｇｕｏＬＩＵ，ＹｉｑｉｎｇＳＨＥＮ（ＩｎｓｔｉｔｕｔｅｏｆＣｏｍｐｕｔａｔｉｏｎａｌＭａｔｈｅｍａｔｉｃ...     

Inverse Hlder Inequality Related to Metrics and It’s Applications to Nonlinear Subelliptic Systems

ＩｎｖｅｒｓｅＨｌｄｅｒＩｎｅｑｕａｌｉｔｙＲｅｌａｔｅｄｔｏＭｅｔｒｉｃｓａｎｄＩｔ’ｓＡｐｐｌｉｃａｔｉｏｎｓｔｏＮｏｎｌｉｎｅａｒＳｕｂｅｌｉｐｔｉｃＳｙｓｔｅｍｓＣｈｅｎＷｅｎｙｉ（陈文艺）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＷｕｈａｎＵｎｉｖ．，Ｗ...     

A Construction of Cartesian Authentication Codes from Vector Space and Dual Authentication Codes

ＡＣｏｎｓｔｒｕｃｔｉｏｎｏｆＣａｒｔｅｓｉａｎＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓｆｒｏｍＶｅｃｔｏｒＳｐａｃｅａｎｄＤｕａｌＡｕｔｈｅｎｔｉｃａｔｉｏｎＣｏｄｅｓＦｅｎｇＲｏｎｇｑｕａｎ（冯荣权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ...     

Variational Inequality and Complementarity Problem for Set－Valued Mapping with Application

ＶａｒｉａｔｉｏｎａｌＩｎｅｑｕａｌｉｔｙａｎｄＣｏｍｐｌｅｍｅｎｔａｒｉｔｙＰｒｏｂｌｅｍｆｏｒＳｅｔ－ＶａｌｕｅｄＭａｐｐｉｎｇｗｉｔｈＡｐｐｌｉｃａｔｉｏｎ￥ＺｈａｎｇＣｏｎｇｊｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｈｕａｉｂｅ...     

Solutions of Superlinear Hammerstein Integral Equation in Banach Spaces and Applications

ＳｏｌｕｔｉｏｎｓｏｆＳｕｐｅｒｌｉｎｅａｒＨａｍｍｅｒｓｔｅｉｎＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｉｎＢａｎａｃｈＳｐａｃｅｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓＬｏｕＢｅｎｄｏｎｇ（娄本东）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，...     

Some Lower Bounds of Bandwidth Sum of Graphs with Applications

ＳｏｍｅＬｏｗｅｒＢｏｕｎｄｓｏｆＢａｎｄｗｉｄｔｈＳｕｍｏｆＧｒａｐｈｓｗｉｔｈＡｐｐｌｉｃａｔｉｏｎｓ￥ＹｕａｎＪｉｎｊｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｚｈｅｎｇｚｈｏｕ，４５００...     

ANewAnisotropick-ModelandItsApplications￣1

ＡＮｅｗＡｎｉｓｏｔｒｏｐｉｃｋ－ＭｏｄｅｌａｎｄＩｔｓＡｐｐｌｉｃａｔｉｏｎｓ￣１ＧｒａｎｇｓｈｅｎｇＺＨＵ，ＧａｎｇＺＨＡＯ＆ＣｈｕｉｊｉｅＷＵ（ＮａｎｊｉｎｇＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙ，２１００９４，Ｎａｎ...     

Some Properties of Quasi-keep-range Operators and Their Applications

ＳｏｍｅＰｒｏｐｅｒｔｉｅｓｏｆＱｕａｓｉ┐ｋｅｅｐ┐ｒａｎｇｅＯｐｅｒａｔｏｒｓａｎｄＴｈｅｉｒＡｐｐｌｉｃａｔｉｏｎｓＬａｉＣｈｕｎｈｕｉ（赖春晖）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｅｇｅ，...     

关于吴方法在双层规划中的一个应用

双层规划及多层规划这一数学规划研究中的较新领域因其坚实的经济背景及丰富的数学内涵在二十年来的发展过程中变得越来越吸引人们的关注. 在通常解双层规划问题时往往采用数值计算的方法, 得到的解并不一定是全局最优解. 该文介绍了一个全新的解双层规划问题的方法,它与数值计算法不同, 采用的是符号计算, 依据了计算机代数与代数几何的理论. 作者通过对文献[1]中的几个双层规划问题的上机计算, 得出了与之不同的全面彻底的解答, 在比较过程中, 发现不仅所得的结果要比文献[1]中答案更进一步, 而且也证明了文章的新方法在解这一类问题时,是简明和行之有效的.     

Singular Perturbation Analysis of Boundary Value Problems for Differential-Difference Equations. IV. A Nonlinear Example with Layer Behavior

A study is made of boundary value problems for a class of singularly perturbed nonlinear, second-order, differential-difference equations, i.e., where the highest-order derivative is multiplied by a small parameter. Depending on the region of parameter space, solutions of the nonlinear problem may not be unique, can exhibit extreme sensitivity to the values of the parameters, or may not exist. Typically, solutions exhibit layer behavior and/or exponentially large amplitudes. Approximate solutions of these boundary value problems are obtained by using singular perturbation methods and numerical computations and are then compared. Numerical computations of representative solutions illustrate the wide variety of possible behaviors.     

A linear programming-based optimization algorithm for solving nonlinear programming problems

In this paper a linear programming-based optimization algorithm called the Sequential Cutting Plane algorithm is presented. The main features of the algorithm are described, convergence to a Karush–Kuhn–Tucker stationary point is proved and numerical experience on some well-known test sets is showed. The algorithm is based on an earlier version for convex inequality constrained problems, but here the algorithm is extended to general continuously differentiable nonlinear programming problems containing both nonlinear inequality and equality constraints. A comparison with some existing solvers shows that the algorithm is competitive with these solvers. Thus, this new method based on solving linear programming subproblems is a good alternative method for solving nonlinear programming problems efficiently. The algorithm has been used as a subsolver in a mixed integer nonlinear programming algorithm where the linear problems provide lower bounds on the optimal solutions of the nonlinear programming subproblems in the branch and bound tree for convex, inequality constrained problems.     

An Adaptive Neural Network Model for Nonlinear Programming Problems

In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.     

冲击接触问题的一种双共振投影梯度算法

根据冲击接触计算模型所需满足的基本控制方程和非线性互补条件,应用非线性互补问题与约束优化的等价关系将非线性互补接触问题转变成一个非线性规划问题,系统地推导建立了冲击接触问题的一种双共轭投影梯度计算方法．增广Lagrange乘子法克服了罚函数要求减小迭代步长以达到计算稳定的限制,即使对于冲击接触问题亦可以采用较大迭代步长,在形成的与原互补问题等价的无约束规划模式下,应用双共轭投影梯度算法提高非线性搜索速度和计算效率．算法模型计算结果表明,所建立的双共轭投影梯度计算理论及方法是正确有效的．     

Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data

This paper focuses on the study of finding efficient solutions in fractional multicriteria optimization problems with sum of squares convex polynomial data. We first relax the fractional multicriteria optimization problems to fractional scalar ones. Then, using the parametric approach, we transform the fractional scalar problems into non-fractional problems. Consequently, we prove that, under a suitable regularity condition, the optimal solution of each non-fractional scalar problem can be found by solving its associated single semidefinite programming problem. Finally, we show that finding efficient solutions in the fractional multicriteria optimization problems is tractable by employing the epsilon constraint method. In particular, if the denominators of each component of the objective functions are same, then we observe that efficient solutions in such a problem can be effectively found by using the hybrid method. Some numerical examples are given to illustrate our results.     

TRUST REGION METHOD IN NEURAL NETWORK

1.IntroductionHopfieldandTank[5]presentedamodeltosolvetravellingsalesmanproblem,thusinitiatingtheapplicationofneuralnetwork(NN)inthefieldofoptimization.SincethenmanyNNmodelshavebeenproposedtosolvelinearprogramming(LP)problems(13,8,11,14,15])andquadraticprogramming(oP)problems([1,8,20]),asLPandoPhavefundamentalimportanceinthetheoryandpracticeofoptimization.Therewerealsoafewmodelsforgeneralnonlinearprogramming(NP)problem([2,6,9,18]).InthispaperwewillpresentaHopfield-typeneuralnetworkmodelw…     

Extended Improved tanh-Function Method for Solving the Nonlinear Physical Problems

By means of the extended improved tanh-function (EITF) method with computerized symbolic computations for constructing new multiple traveling wave solutions for some different kinds of nonlinear physical problems are presented and implemented. The solutions for the nonlinear equations such as Coupled MKdV and Coupled Hirota-Satsuma Coupled KdV equations which include new trigonometric function solutions and rational solutions are exactly obtained. So consequently, the efficiency of the method can be demonstrated.     

基于S-R和分解定理的几何非线性问题的数值计算分析

为了探究几何非线性问题的数值求解方法,采用理论推导、MATLAB编程计算、有限元模拟相结合的方法,基于S-R和分解定理及更新拖带坐标描述法,运用插值型无单元Galerkin方法对几何非线性问题的增量变分方程进行了推导,并通过四点Gauss积分法和不动点迭代法对其进行求解.最后以平面悬臂梁的大变形问题为例进行求解计算,发现与ANSYS的计算结果拟合相似度很高,说明了所采用的几何非线性力学理论及数值计算方法的正确性和合理性,为求解几何非线性问题提供了一种新的依据.     

A Generalization of the Karush–Kuhn–Tucker Theorem for Approximate Solutions of Mathematical Programming Problems Based on Quadratic Approximation

In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary δ-optimality condition in the smooth mathematical programming problem that generalizes the Karush–Kuhn–Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.