# 管理科学代写|决策论代写Management Science Models for Decision Making代考|OPMT3197

#### Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes-lab™ 为您的留学生涯保驾护航 在代写决策论Management Science Models for Decision Making方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写决策论Management Science Models for Decision Making代写方面经验极为丰富，各种代写决策论Management Science Models for Decision Making相关的作业也就用不着说。

• 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
couryes™为您提供可以保分的包课服务

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Convex and Concave Functions

A real-valued function $g(y)$ defined over some convex subset $\Gamma \subset R^n$ ( $\Gamma$ may be $R^n$ itself) is said to be a convex function if
$$g\left(\alpha y^1+(1-\alpha) y^2\right) \leq \alpha g\left(y^1\right)+(1-\alpha) g\left(y^2\right)$$
for all $y^1, y^2 \in \Gamma$, and $0 \leq \alpha \leq 1$. This inequality defining a convex function is called Jensen’s inequality after the Danish mathematician who introduced it.

To interpret Jensen’s inequality geometrically, introduce an $(n+1)$ th axis for plotting the function value. So points in this space $R^{n+1}$ are $\left(y, y_{n+1}\right)^T$, where on the $y_{n+1}$ th axis we plot the function value $g(y)$ to get a geometric representation of the function.

The set of all points $\left{(y, g(y))^T: y \in \Gamma\right}$ in this space $R^{n+1}$ is a surface, which is the surface or graph of the function $g(y)$.

The line segment $\left{\left(\alpha y^1+(1-\alpha) y^2, \alpha g\left(y^1\right)+(1-\alpha) g\left(y^2\right)\right)^T: 0 \leq \alpha \leq 1\right}$ joining the two points $\left(y^1, g\left(y^1\right)\right)^T,\left(y^2, g\left(y^2\right)\right)^T$ on the graph of the function is called the chord of the function between the points $y^1, y^2$ or on the one-dimensional line interval joining $y^1$ and $y^2$. If we plot the function curve and the chord on the line segment $\left{\alpha y^1+(1-\alpha) y^2: 0 \leq \alpha \leq 1\right}$, then Jensen’s inequality requires that the function curve lie beneath the chord. See Fig. $2.1$ where the function curve and a chord are shown for a function $\theta(\lambda)$ of one variable $\lambda$.

The real-valued function $h(y)$ defined on a convex subset $\Gamma \subset R^n$ is said to be a concave function if $-h(y)$ is a convex function, that is, if
$$h\left(\alpha y^1+(1-\alpha) y^2\right) \geq \alpha h\left(y^1\right)+(1-\alpha) h\left(y^2\right)$$
for all $y^1, y^2 \in \Gamma$ and $0 \leq \alpha \leq 1$; see Fig. 2.2. For a concave function $h(y)$, the function curve always lies above every chord.

## 管理科学代写|决策论代写Management Science Models for Decision Making代考|Piecewise Linear (PL) Functions

Definition: Piecewise Linear (PL) Functions: Considering real-valued continuous functions $f(x)$ defined over $R^n$, these are nonlinear functions that may not satisfy the linearity assumptions over the whole space $R^n$, but there is a partition of $R^n$ into convex polyhedral regions, say $R^n=K_1 \cup K_2 \cup \ldots \cup K_r$ such that $f(x)$ is an affine function within each of these regions individually, that is, for each $1 \leq t \leq r$
there exist constants $c_0^t, c^t=\left(c_1^t, \ldots, c_n^t\right)$ such that $f(x)=f_t(x)=c_0^t+c^t x$ for all $x \in K_t$, and for every $S \subset{1, \ldots, r}$, and at every point $x \in \cap_{t \in S} K_t$, the different functions $f_t(x)$ for all $t \in S$ have the same value.

Now we give some examples of continuous PL functions defined over $R^1$. Denote the variable by $\lambda$.

Each convex polyhedral subset of $R^1$ is an interval; so a partition of $R^1$ into convex polyhedral subsets expresses it as a union of intervals: $\left[-\infty, \lambda_1\right]={\lambda: \lambda \leq$ $\left.\lambda_1\right},\left[\lambda_1, \lambda_2\right]=\left{\lambda: \lambda_1 \leq \lambda \leq \lambda_2\right}, \ldots,\left[\lambda_{r-1}, \lambda_r\right],\left[\lambda_r, \infty\right]$, where $\lambda_1, \ldots, \lambda_r$ are the boundary points of the various intervals, usually called the breakpoints in this partition.

The function $\theta(\lambda)$ is a PL function if there exists a partition of $R^1$ like this such that inside each interval of this partition the slope of $\theta(\lambda)$ is a constant, and its value at each breakpoint agrees with the limits of $\theta(\lambda)$ as $\lambda$ approaches this breakpoint from the left, or right; that is, it should be of the form tabulated below:

Notice that the PI function $\theta(\lambda)$ defined in the table above is continuous, and at ēāch of thẻ breảkpooints $\bar{\lambda} \in\left{\lambda_1 \ldots . \lambda_r\right}$ wẻ vërify thả
$$\lim {\epsilon \rightarrow 0^{-}} \theta(\bar{\lambda}+\epsilon)=\lim {\epsilon \rightarrow 0^{+}} \theta(\bar{\lambda}+\epsilon)=\theta(\bar{\lambda}) .$$
Here are numerical examples of continuous PL functions:
Example 2.1.

# 决策论代写

## 管理科学代写|决策论代写管理科学决策模型代考|凸函数和凹函数

$$g\left(\alpha y^1+(1-\alpha) y^2\right) \leq \alpha g\left(y^1\right)+(1-\alpha) g\left(y^2\right)$$
，则称其为凸函数。这个定义凸函数的不等式被称为延森不等式，以引入它的丹麦数学家的名字命名

$$h\left(\alpha y^1+(1-\alpha) y^2\right) \geq \alpha h\left(y^1\right)+(1-\alpha) h\left(y^2\right)$$
，则称其为凹函数;见图2.2。对于凹函数$h(y)$，函数曲线总是位于每个弦的上方

## 管理科学代写|决策论代写管理科学决策模型代考|分段线性(PL)函数

$$\lim {\epsilon \rightarrow 0^{-}} \theta(\bar{\lambda}+\epsilon)=\lim {\epsilon \rightarrow 0^{+}} \theta(\bar{\lambda}+\epsilon)=\theta(\bar{\lambda}) .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

Days
Hours
Minutes
Seconds

# 15% OFF

## On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)