### 数学代写|线性规划作业代写Linear Programming代考|MATH3202

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|线性规划作业代写Linear Programming代考|Linear Programming

Linear programming, hereafter LP , is without doubt the most natural mechanism for formulating a vast array of problems with modest effort. A linear programming problem is characterized, as the name implies, by linear functions of the unknowns; the objective is linear in the unknowns, and the constraints are linear equalities or linear inequalities in the unknowns. One familiar with other branches of linear mathematics might suspect, initially, that linear programming formulations are popular because the mathematics is nicer, the theory is richer, and the computation simpler for linear problems than for nonlinear ones. But, in fact, these are not the primary reasons. In terms of mathematical and computational properties, there are much broader classes of optimization problems than linear programming problems that have elegant and potent theories and for which effective algorithms are available. It seems that the popularity of linear programming lies primarily with the formulation phase of analysis rather than the solution phase-and for good cause. For one thing, a great number of constraints and objectives that arise in practice are indisputably linear. Thus, for example, if one formulates a problem with a budget constraint restricting the total amount of money to be allocated among two different commodities, the budget constraint takes the form $x_{1}+x_{2} \leq B$, where $x_{j}, i=1,2$,

is the amount allocated to activity $i$, and $B$ is the budget. Similarly, if the objective is, for example, maximum weight, then it can be expressed as $w_{1} x_{1}+w_{2} x_{2}$, where $w_{j}, i=1,2$, is the unit weight of the commodity $i$. The overall problem would be expressed as
$\operatorname{maximize} w_{1} x_{1}+w_{2} x_{2}$
subject to $x_{1}+x_{2} \leq B$,
$$x_{1} \geq 0, x_{2} \geq 0 \text {, }$$
which is an elementary linear program. The linearity of the budget constraint is extremely natural in this case and does not represent simply an approximation to a more general functional form.

Another reason that linear forms for constraints and objectives are so popular in problem formulation is that they are often the least difficult to define. Thus, even if an objective function is not purely linear by virtue of its inherent definition (as in the above example), it is often far easier to define it as being linear than to decide on some other functional form and convince others that the more complex form is the best possible choice. Linearity, therefore, by virtue of its simplicity, often is selected as the easy way out or, when seeking generality, as the only functional form that will be equally applicable (or nonapplicable) in a class of similar problems.

Of course, the theoretical and computational aspects do take on a somewhat special character for linear programming problems – the most significant development being the simplex method. This algorithm is developed in Chaps. 2 and 4. More recent interior point methods are nonlinear in character and these are developed in Chap. $5 .$

## 数学代写|线性规划作业代写Linear Programming代考|Conic Linear Programming

Conic Linear Programming, hereafter CLP, is a natural extension of linear programming. In LP, the variables may form a vector or point that is subjected to be componentwise nonnegative, while in CLP they form a point in a general pointed convex cone (see Appendix B.1) of an Euclidean space, such as a vector or a matrix of finite dimensions. Consider the three optimization problems below:

While these problems share the identical linear objective function and single linear equality constraint, the three variables form a point in three different cones as indicated by the bottom constraint: on the left they form a vector in the nonnegative orthant cone, in the middle they form a vector in a cone shaped like an ice cream cone, called a second-order cone, and on the right they form a 2-dimensional symmetric matrix required to be positive semidefinite or to be in a semidefinite cone.

Optimization problems involving quadratic functions may be formulated as problems with the second-order cone constraint, hereafter SOCP , which find wide applications in Financial Engineering. Optimization problems involving a variable matrix, like matrix completion in Machine Learning and covariance matrix estimation in Statistics, may be formulated as problems with the semidefinite cone constraint, hereafter SDP. Many applications and solution methods will be discussed in Chap. $6 .$

## 数学代写|线性规划作业代写Linear Programming代考|Linear Programming

maximize $w_{1} x_{1}+w_{2} x_{2}$

$$x_{1} \geq 0, x_{2} \geq 0$$

## 数学代写|线性规划作业代写Linear Programming代考|Conic Linear Programming

CONIC线性编程，以下是CLP，是线性编程的自然扩展。在 LP 中，变量可以形成一个向量或点，该向量或点是按分量非负的，而在 CLP 中，它们在欧几里得空间的一般凸锥（见附录 B.1）中形成一个点，例如向量或有限尺寸的矩阵。考虑以下三个优化问题：

## 有限元方法代写

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## 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。