19th Ave New York, NY 95822, USA

# 数学代写|优化理论代写Optimization Theory代考|Inserting a new inequality (cut)

my-assignmentexpert™提供最专业的一站式服务：Essay代写，Dissertation代写，Assignment代写，Paper代写，Proposal代写，Proposal代写，Literature Review代写，Online Course，Exam代考等等。my-assignmentexpert™专注为留学生提供Essay代写服务，拥有各个专业的博硕教师团队帮您代写，免费修改及辅导，保证成果完成的效率和质量。同时有多家检测平台帐号，包括Turnitin高级账户，检测论文不会留痕，写好后检测修改，放心可靠，经得起任何考验！

## 数学代写|优化理论代写Optimization Theory代考|Inserting a new inequality (cut)

Because the solution set of a linear inequality is a halfspace – and hence divides $n$-space into two parts – an inequality is sometimes called a cut, especially when it is adjoined to another set of constraints.

The Dual Simplex Algorithm is frequently applied within other algorithms when a linear program has been solved and then a new inequality constraint is adjoined to the system after the optimization has been carried out. Let’s see how this works. Suppose we have just solved the problem
$$\begin{array}{ll} \text { minimize } & c^{\mathrm{T}} x \ \text { subject to } & A x=b \ & x \geq 0 \end{array}$$
and found an optimal basis, $B$. For ease of discussion, we assume that $B=\left[\begin{array}{llll}A_{.1} & A_{.2} & \cdots & A_{. m}\end{array}\right]$ and we have the problem written in canonical form with respect to this basis as expressed in the tableau
\begin{tabular}{|l||ccc|c||l|}
\hline $\min$ & $z$ & $x_B$ & $x_N$ & 1 & basic \
\hline \hline row 0 & 1 & $0^{\mathrm{T}}$ & $\bar{c}N^{\mathrm{T}}$ & $c_B^{\mathrm{T} \bar{b}}$ & $z$ \ \hline rows $1, \ldots, m$ & 0 & $I$ & $\bar{A} \bullet{\bullet N}$ & $\bar{b}$ & $x_B$ \
\hline
\end{tabular}
Now suppose we adjoin a linear inequality of the form
$$a_B^{\mathrm{T}} x_B+a_N^{\mathrm{T}} x_N \leq d .$$

## 数学代写|优化理论代写Optimization Theory代考|Deleting an activity

Deleting an activity from the model after an optimal solution has been found presents two cases; these correspond to whether or not the activity to be deleted is basic. If the column of the deleted activity is nonbasic, there is no change in the optimal value because the value of the corresponding nonbasic variable is zero. It is only when the activity to be deleted corresponds to a basic variable that issues come up. The first of these is simply one of feasibility, for it may happen that the problem becomes infeasible without the deleted column. Another possibility could be that the variable corresponding to the activity is basic but has value zero (as in a degenerate basic feasible solution).

It should be noted that the elimination of an activity can be viewed as the equivalent of forcing the corresponding variable to have the value zero. Since in standard form, all the decision variables are nonnegative, we can force the variable $x_k$ to be zero by adding the cut $x_k \leq 0$.

## 数学代写|优化理论代写OPTIMIZATION THEORY代 考|INSERTING A NEW INEQUALITY $c u t$

$$\text { minimize } \quad c^{\mathrm{T}} x \text { subject to } A x=b \quad x \geq 0$$

$$a_B^{\mathrm{T}} x_B+a_N^{\mathrm{T}} x_N \leq d .$$

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。