线性规划问题退化最优基可行解的性质

本通过分析两用阶段法求解线性规划初始可行解的一个例子,归纳了线性规划问题退化的最优基可行解的性质,包括同一退化最优基可行解不同表示,有无穷多最优解的表示。     

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.     

线性规划最优解集的表现

文献［１］讨论了有无穷多最优解的线性规划问题，并利用最优单纯形表格的检验数给出线性规划有无穷多最优解的判别法，本文利用最优基可行解的凸组合及最优极向的非负线性组合给出线性规划最优解集的表现，从而把线性规划最优解集的几何特征阐释清楚．     

双层线性规划的一个全局优化方法

用线性规划对偶理论分析了双层线性规划的最优解与下层问题的对偶问题可行域上极点之间的关系，通过求得下层问题的对偶问题可行域上的极点，将双层线性规划转化为有限个线性规划问题，从而用线性规划方法求得问题的全局最优解．由于下层对偶问题可行域上只有有限个极点，所以方法具有全局收敛性．     

线性规划可行解的一个性质

通过对线性规划问题可行解的性质的推广,导出推广后的可行解与对应的对偶线性规划的约束条件之间互为充分必要的关系。     

实时求解线性规划问题的原对偶神经网络(英文)

本文探讨了线性规划的原问题与对偶问题理论,并在此基础上可开发出一种用于在线求解线性规划的递归神经网络和应用于冗余机器手臂逆运动学的求解问题上.如,Tang等人开展的原对偶神经网络.但鉴于对偶理论的复杂性和多样性,该原对偶神经网络模型仅可以得到线性规划问题的可行解,而本文对该网络模型改进后可得到线性规划问题的最优解.仿真结果证实了这种改进模型在解决线性规划问题上的有效性、正确性和高效率.     

线性规划应用中的优值调整

人教版高中数学试验本第二册 (上 )增加了“简单的线性规划”这部分内容 ,在线性规划的实际应用中 ,理论上得到的最优解有时可能不满足实际要求 ,这时就需要进行优值调整 .本文将归纳优值调整的几种常用方法 ,供参考 .　　一、在可行域内 ,找出可能成为最优解的所有可行解 ,逐个代入目标函数验证 ,确定出实际最优解 .这种方法适用于可行域内这种可能成为最优解的可行解不太多的问题 .例 1　某运输公司有 7辆载重量为 6ｔ的Ａ型卡车和 4辆载重量为 1 0ｔ的Ｂ型卡车 ,有9名驾驶员 .在建筑某段高速公路中 ,此公司承包了每天至少搬运 36 0ｔ沥青…     

利用整点折线边界解一类线性规划问题

线性规划问题中的最优解的常用求法是图象法,如没有特殊要求,最优解一般会在可行域的边界点处取得.但是,对于最优解必须是整数的线性规划问题,有时在原边界处取不到最优解.对于这种情况,现行课本及资料提供的方法,一是以取得非整数最优解的线     

线性规划问题的矩阵求解方法

单纯形法是求解线性规划问题的基本方法。它的解题思路是,先求一个可行解,经过检验如果不是最优解,则从这个可行解转换到另一个可行解。若后者仍不是最优解,再重复上述     

直接求线性规划可行基的一种方法

本文给出直接求线性规划问题基可行解的一种简易方法,该方法既避免了引入人工变量,减少存储,一般又能较快地得到一个较好的基可行解.     

A multiobjective based approach for mathematical programs with linear flexible constraints

In this paper a mathematical problem with linear flexible constraints is considered. In order to solve the problem an approach is proposed based on multiobjective linear programming. Indeed, allowing violations for the constraints, and using multiobjective linear programming to minimize these violations, a subset of solution set which has less violations, namely efficiently feasible set, is obtained. Then, the corresponding objective function is optimized over efficiently feasible set in order to obtain an optimal solution. An application of the proposed approach in pattern classification is introduced.     

Some new results in linear programs with trapezoidal fuzzy numbers: Finite convergence of the Ganesan and Veeramani’s method and a fuzzy revised simplex method

In a recent paper, Ganesan and Veermani [K. Ganesan, P. Veeramani, Fuzzy linear programs with trapezoidal fuzzy numbers, Ann. Oper. Res. 143 (2006) 305–315] considered a kind of linear programming involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems and then proved fuzzy analogues of some important theorems of linear programming that lead to a new method for solving fuzzy linear programming (FLP) problems. In this paper, we obtain some another new results for FLP problems. In fact, we show that if an FLP problem has a fuzzy feasible solution, it also has a fuzzy basic feasible solution and if an FLP problem has an optimal fuzzy solution, it has an optimal fuzzy basic solution too. We also prove that in the absence of degeneracy, the method proposed by Ganesan and Veermani stops in a finite number of iterations. Then, we propose a revised kind of their method that is more efficient and robust in practice. Finally, we give a new method to obtain an initial fuzzy basic feasible solution for solving FLP problems.     

不需加人工变量的两阶段法

A method is provided to achieve an initial basic feasible solution of a linear programming in this paper. This method dose not need introducing any artificial variable, but needs only solving an auxiliary linear programming. Compared with the traditional two-phase method, it has advantages of saving the memories and reducing the computational efforts.     

Improved integer programming bounds using intersections of corner polyhedra

Consider the relaxation of an integer programming (IP) problem in which the feasible region is replaced by the intersection of the linear programming (LP) feasible region and the corner polyhedron for a particular LP basis. Recently a primal-dual ascent algorithm has been given for solving this relaxation. Given an optimal solution of this relaxation, we state criteria for selecting a new LP basis for which the associated relaxation is stronger. These criteria may be successively applied to obtain either an optimal IP solution or a lower bound on the cost of such a solution. Conditions are given for equality of the convex hull of feasible IP solutions and the intersection of all corner polyhedra.     

Interval solution of nonlinear equations using linear programming

A new computational test is proposed for nonexistence of a solution to a system of nonlinear equations in a convex polyhedral regionX. The basic idea proposed here is to formulate a linear programming problem whose feasible region contains all solutions inX. Therefore, if the feasible region is empty (which can be easily checked by Phase I of the simplex method), then the system of nonlinear equations has no solution inX. The linear programming problem is formulated by surrounding the component nonlinear functions by rectangles using interval extensions. This test is much more powerful than the conventional test if the system of nonlinear equations consists of many linear terms and a relatively small number of nonlinear terms. By introducing the proposed test to interval analysis, all solutions of nonlinear equations can be found very efficently. This work was partially supported by the Japanese Ministry of Education.     

一种具有非线性约束线性规划全局优化算法

本文提出了一种新的适用于处理非线性约束下线性规划问题的全局优化算法。该算法通过构造子问题来寻找优于当前局部最优解的可行解。该子问题可通过模拟退火算法来解决。通过求解一系列的子问题,当前最优解被不断地更新,最终求得全局最优解。最后,本算法应用于几个典型例题,并与罚函数法相比较,数值结果表明该算法是可行的,有效的。     

A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem

The linear semidefinite programming problem is considered. The dual affine scaling method in which all current iterations belong to the feasible set is proposed for its solution. Moreover, the boundaries of the feasible set may be reached. This method is a generalization of a version of the affine scaling method that was earlier developed for linear programs to the case of semidefinite programming.     

A convergent criss-cross method

Our paper presents a new Criss-Cross method for solving linear programming problems. Starting from a neither primal nor dual feasible solution, we reach an optimal solution in finite number of steps if it exists. If there is no optimal solution, then we show that there is not primal feasible or dual feasible solution, We prove the finiteness of this procedure. Our procedure is not the same as the primal or dual simplex method if we have a primal or dual feasible solution, so we have constructed a quite new procedure for solving linear programming problems.     

Max-min resource allocation

A problem is considered of the allocation of resources so as to maximize the minimum return from several activities. Optimality conditions are given for the case of a single resource, and are used to derive a solution algorithm. Problems with several resources cannot be solved by resourcewise optimization. Concave return functions are treated approximately by linear programming, and optimality or almost optimality of any feasible solution to such a problem can be evaluated by the solution of a linear programming problem. The evaluation measure is extended to certain feasible solutions of problems which have continuous, but not necessarily concave, return functions. A numerical example is given.