### 数学代写|线性规划作业代写Linear Programming代考|MAT2200

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Unconstrained Problems

It may seem that unconstrained optimization problems are so devoid of structural properties as to preclude their applicability as useful models of meaningful problems. Quite the contrary is true for two reasons. First, it can be argued, quite convincingly, that if the scope of a problem is broadened to the consideration of all relevant decision variables, there may then be no constraints-or put another way, constraints represent artificial delimitations of scope, and when the scope is broadened the constraints vanish. Thus, for example, it may be argued that a budget constraint is not characteristic of a meaningful problem formulation; since by borrowing at some interest rate it is always possible to obtain additional funds, and hence rather than introducing a budget constraint, a term reflecting the cost of funds should be incorporated into the objective. A similar argument applies to constraints describing the availability of other resources which at some cost (however great) could be supplemented.

The second reason that many important problems can be regarded as having no constraints is that constrained problems are sometimes easily converted to unconstrained problems. For instance, the sole effect of equality constraints is simply to limit the degrees of freedom, by essentially making some variables functions of others. These dependencies can sometimes be explicitly characterized, and a new problem having its number of variables equal to the true degree of freedom can be determined. As a simple specific example, a constraint of the form $x_{1}+x_{2}=B$ can be eliminated by substituting $x_{2}=B-x_{1}$ everywhere else that $x_{2}$ appears in the problem.

Aside from representing a significant class of practical problems, the study of unconstrained problems, of course, provides a stepping stone toward the more general case of constrained problems. Many aspects of both theory and algorithms are most naturally motivated and verified for the unconstrained case before progressing to the constrained case.

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

In spite of the arguments given above, many problems met in practice are formulated as constrained problems. This is because in most instances a complex problem such as, for example, the detailed production policy of a giant corporation, the planning of a large government agency, or even the design of a complex device cannot be directly treated in its entirety accounting for all possible choices, but instead must be decomposed into separate subproblems-each subproblem having constraints that are imposed to restrict its scope. Thus, in a planning problem, budget constraints are commonly imposed in order to decouple that one problem from a more global one. Therefore, one frequently encounters general nonlinear constrained mathematical programming problems.
The general mathematical programming problem can be stated as
In this formulation, $\mathbf{x}$ is an $n$-dimensional vector of unknowns, $\mathbf{x}=\left(x_{1}, x_{2}, \ldots\right.$, $\left.x_{n}\right)$, and $f, h_{i}, i=1,2, \ldots, m$, and $g_{j}, j=1,2, \ldots, p$, are real-valued functions of the variables $x_{1}, x_{2}, \ldots, x_{n}$. The set $S$ is a subset of $n$-dimensional space. The function $f$ is the objective function of the problem and the equations, inequalities, and set restrictions are constraints.

Generally, in this book, additional assumptions are introduced in order to make the problem smooth in some suitable sense. For example, the functions in the problem are usually required to be continuous, or perhaps to have continuous derivatives. This ensures that small changes in $\mathbf{x}$ lead to small changes in other values associated with the problem. Also, the set $S$ is not allowed to be arbitrary but usually is required to be a connected region of $n$-dimensional space, rather than, for example, a set of distinct isolated points. This ensures that small changes in $\mathbf{x}$ can be made. Indeed, in a majority of problems treated, the set $S$ is taken to be the entire space; there is no set restriction.

In view of these smoothness assumptions, one might characterize the problems treated in this book as continuous variable programming, since we generally discuss problems where all variables and function values can be varied continuously. In fact, this assumption forms the basis of many of the algorithms discussed, which operate essentially by making a series of small movements in the unknown $\mathbf{x}$ vector.

## 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。