一种用于线性规划算法的换基准则

本文就线性规划中的对偶单纯形法和运输问题中的表上作业法选取出基变量或者对基变量的准则进行改进,从而得出一种新的换基准则.按该方法进行优化运算,可以使算法的迭代次数减到最少,从而加快了运算速度.     

运输问题表上作业法的一点注记

表上作业法是运输问题的经典算法,然而按照表上作业法闭回路构建方法有时竟然不能成功,为此本文重新设计了新的闭回路构建方法,改进了表上作业法.     

可行下降视角下退化运输问题的最优性条件

运输问题是一类特殊的线性规划问题,通常用特殊的单纯形法—运输单纯形法(也叫表上作业法)进行求解,其最优性条件为所有非基变量的检验数大于等于零.针对实际算例中出现的某个非基变量的检验数小于零,却已经达到最优的情况,从可行下降方向的角度进行了探讨.结论表明:一般情况下非基变量的检验数大于等于零仅是运输问题最优解的充分条件;而问题非退化时,该判别条件成为充要条件.     

一类线性规划问题初始可行基产生的新方法

本对一类特殊的线性规划问题提出了利用最优基的启发性刻划产生初始基，进而用无比检验规则产生初始可行基的方法，并给出了此方法在单纯形表上实现的步骤。     

运输问题图上作业法的破圈技巧

图上作业法是借助流向图进行物流合理规划的简便线性规划方法.对于有圈交通图,“舍边破圈”是用图上作业法解决平衡运输问题的关键.将对运输问题图上作业法的破圈技巧展开探讨,梳理了几种常用的破圈技巧,并通过若干反例说明了常用的破圈技巧其效果的不确定性,最后给出了相对合理可行的破圈调整技巧.     

实矩阵特征值排序的直接算法

矩阵不变子空间的计算是求解矩阵特征值问题的继续。近年来发展的计算不变子空间的正交基或更一般的稳定基的算法中,常需解决将特征值按要求的次序排列的问题,不妨称之为排序问题。对於复矩阵,不变子空间的稳定基的计算是首先应用QR方法将矩阵经酉相似变换约化为上三角阵,而对上三角阵Ruhe提出了一个简单而有效     

产销平衡运输问题的表上作业法解法的一个注记

本文给出了用表上作业法求解产销平衡运输问题当出现退化时在相应空格填“O”的更为明确的规则，利用该规则可以避免可能存在的多余计算。本文还给出了用改进后的表上作业法求解指派问题的方法和步骤，该方法与求解指派问题的常用方法“匈牙利法”相比，具有手工计算更为简便的优点。     

求Hermite型插值的广义Lagrange基函数方法

在求解各类插值问题时候,各种不同方法的本质是基函数的构造不同.本文提出了每个节点上的广义La-grange基函数概念,从数据表列的角度出发给出了一种求解各类Hermite插值问题的新方法,并通过各种算例进行了验证.     

初始可行基的判定

用高等数学的理论和方法,对无初始可行基的线性规划问题解的存在性及求解方法进行研究,得出关于无初始可行基的线性规划问题解的存在性的六个定理,回答了无初始可行基的线性规划问题解的存在条件和该问题的初始可行基的确定方法.     

表上作业法在团体比赛项目中的应用

借助解运输问题的表上作业法,研究集体比赛项目中参赛队员的出场次序问题,从而为教练员排兵布阵提供一种科学的决策方法.     

On solving biquadratic optimization via semidefinite relaxation

A method called PAINT is introduced for computationally expensive multiobjective optimization problems. The method interpolates between a given set of Pareto optimal outcomes. The interpolation provided by the PAINT method implies a mixed integer linear surrogate problem for the original problem which can be optimized with any interactive method to make decisions concerning the original problem. When the scalarizations of the interactive method used do not introduce nonlinearity to the problem (which is true e.g., for the synchronous NIMBUS method), the scalarizations of the surrogate problem can be optimized with available mixed integer linear solvers. Thus, the use of the interactive method is fast with the surrogate problem even though the problem is computationally expensive. Numerical examples of applying the PAINT method for interpolation are included.     

Reconstruction of boundary regimes in the inverse problem of thermal convection of a high-viscosity fluid

A problem of reconstruction of boundary regimes in a model for free convection of a high-viscosity fluid is considered. A variational method and a quasi-inversion method are suggested for solving the problem in question. The variational method is based on the reduction of the original inverse problem to some equivalent variational minimum problem for an appropriate objective functional and solving this problem by a gradient method. When realizing the gradient method for finding a minimizing element of the objective functional, an iterative process actually reducing the original problem to a series of direct well-posed problems is organized. For the quasi-inversion method, the original differential model is modified by means of introducing special additional differential terms of higher order with small parameters as coefficients. The new perturbed problem is well-posed; this allows one to solve this problem by standard methods. An appropriate choice of small parameters gives an opportunity to obtain acceptable qualitative and quantitative results in solving the inverse problem. A comparison of the methods suggested for solving the inverse problem is made with the use of model examples.     

A semidefinite programming approach for solving fractional optimal control problems

This paper presents a numerical scheme for solving fractional optimal control. The fractional derivative in this problem is in the Riemann–Liouville sense. The proposed method, based upon the method of moments, converts the fractional optimal control problem to a semidefinite optimization problem; namely, the nonlinear optimal control problem is converted to a convex optimization problem. The Grunwald–Letnikov formula is also used as an approximation for fractional derivative. The solution of fractional optimal control problem is found by solving the semidefinite optimization problem. Finally, numerical examples are presented to show the performance of the method.     

Revision of distance minimization method for ranking of fuzzy numbers

Asady and Zendehnam employed “distance minimization” to ranking fuzzy numbers in Ref [1]. Then Abbasbandy and Hajjari in [2] found a problem of its. To overcome it problem, they proposed magnitude method to ranking fuzzy numbers. Unfortunately, their method can not to overcome this problem. In this paper, we want to indicate this problem and then propose a revise method of distance minimization method which can avoid problem for ranking fuzzy numbers. Since the revised method is based on the distance minimization method, it is easy to rank fuzzy numbers in a way similar to the original method.     

An optimization method for solving some differential algebraic equations

In this paper, the problem of differential algebraic equations has been solved via Chebyshev integral method combined with an optimization method. Two approaches are used based on the index of the problem: in the first, the proposed method is applied on the original problem and in the second, the index of the problem is decreased and the modified problem is solved. An optimization technique is proposed to solve the resulting algebraic equations. Numerical results are included to confirm the efficiency and accuracy of the method.     

Steklov特征值问题的边界元近似

本文将Ｌａｐｌａｃｅ算子的Ｓｔｅｋｌｏｖ特征值问题归化为一个边界变分问题，从而使原问题的空间维数降低了一维，基于此变分问题给出了Ｓｔｅｋｌｏｖ特征值问题的边界元近似解，计算实例表明此方法是十分有效的。     

双层规划问题的一种模式搜索Filter方法

双层规划在工程设计和经济管理中应用广泛,结合模式搜索方法和Filter方法提出了一种解决双层规划问题的算法—模式搜索Filter方法.算法以Filter法思想构造接受准则,以模式搜索提供迭代方向和步长,能够有效的解决一类双层规划问题.     

A novel numerical method and its convergence for nonlinear delay Volterra integro-differential equations

In this paper, we suggest a convergent numerical method for solving nonlinear delay Volterra integro-differential equations. First, we convert the problem into a continuous-time optimization problem and then use a shifted pseudospectral method to discrete the problem. Having solved the last problem, we can achieve the pointwise and continuous approximate solutions for the main delay Volterra integro-differential equations. Here, we analyze the convergence of the method and solve some numerical examples to show the efficiency of the method.     

应用迭代法求解一类非线性问题

本文应用迭代法求解一类有限维非线性问题,该方法是求解线性问题的雅可比迭代法在非线性问题上的推广,且此迭代方法具有几何收敛性质.     

Nonclassical pseudospectral method for the solution of brachistochrone problem

In this paper, nonclassical pseudospectral method is proposed for solving the classic brachistochrone problem. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Properties of nonclassical pseudospectral method are presented, these properties are then utilized to reduce the computation of brachistochrone problem to the solution of algebraic equations. Using this method, the solution to the brachistochrone problem is compared with those in the literature.