assignmentutor™您的专属作业导师

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写组合优化Combinatorial optimization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。我们的专家在代写组合优化Combinatorial optimization代写方面经验极为丰富，各种代写组合优化Combinatorial optimization相关的作业也就用不着说。

• 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|组合优化代写Combinatorial optimization代考|Linear Programming Algorithms

Three types of algorithms for LINEAR PROGRAMMING had the most impact: the SIMPLEX ALGORITHM (see Section 3.2), interior point algorithms, and the ElLIPSOID METHOD.

Each of these has a disadvantage: In contrast to the other two, so far no variant of the Simplex AlgORITHM has been shown to have a polynomial running time. In Sections $4.4$ and $4.5$ we present the ElLIPSOID METHOD and prove that it leads to a polynomial-time algorithm for Linear ProgramMING. However, the ElLIPSOID METHOD is too inefficient to be used in practice. Interior point algorithms and, despite its exponential worst-case running time, the SIMPLEX ALGORITHM are far more efficient, and they are both used in practice to solve LPs. In fact, both the ELLIPSOID METHOD and interior point algorithms can be used for more general convex optimization problems, e.g. for so-called semidefinite programs.

An advantage of the Simplex AlgORITHM and the ElLIPSOID METHOD is that they do not require the LP to be given explicitly. It suffices to have an oracle (a subroutine) which decides whether a given vector is feasible and, if not, returns a violated constraint. We shall discuss this in detail with respect to the ELLIPSOID METHOD in Section 4.6, because it implies that many combinatorial optimization problems can be solved in polynomial time; for some problems this is in fact the only known way to show polynomial solvability. This is the reason why we discuss the ElLIPSOID METHOD but not interior point algorithms in this book.

A prerequisite for polynomial-time algorithms is that there exists an optimum solution that has a binary representation whose length is bounded by a polynomial in the input size. We prove in Section $4.1$ that this condition holds for Linear PROGRAMMING. In Sections $4.2$ and $4.3$ we review some basic algorithms needed later, including the well-known Gaussian elimination method for solving systems of equations.

## 数学代写|组合优化代写Combinatorial optimization代考|Continued Fractions

When we say that the numbers occurring in a certain algorithm do not grow too fast, we often assume that for each rational $\frac{p}{q}$ the numerator $p$ and the denominator $q$ are relatively prime. This assumption causes no problem if we can easily find the greatest common divisor of two natural numbers. This is accomplished by one of the oldest algorithms:
(1) While $p>0$ and $q>0$ do:
If $p<q$ then set $q:=q-\left\lfloor\frac{q}{p}\right\rfloor p$ else set $p:=p-\left\lfloor\frac{p}{q}\right\rfloor q$.
(2) $\operatorname{Return} d:=\max {p, q}$.
Theorem 4.6. The EUCLIDEAN ALGORITHM works correctly. The number of iterations is at most $\operatorname{size}(p)+\operatorname{size}(q)$.

Proof: The correctness follows from the fact that the set of common divisors of $p$ and $q$ does not change throughout the algorithm, until one of the numbers becomes zero. One of $p$ or $q$ is reduced by at least a factor of two in each iteration, hence there are at most $\log p+\log q+1$ iterations.

Since no number occurring in an intermediate step is greater than $p$ and $q$, we have a polynomial-time algorithm.

A similar algorithm is the so-called CONTINUED FRACTION EXPANSION. This can be used to approximate any number by a rational number whose denominator is not too large. For any positive real number $x$ we define $x_0:=x$ and $x_{i+1}:=\frac{1}{x_i-\left[x_i\right\rfloor}$ for $i=1,2, \ldots$, until $x_k \in \mathbb{N}$ for some $k_{.}$. Then we have
$$x=x_0=\left\lfloor x_0\right\rfloor+\frac{1}{x_1}=\left\lfloor x_0\right\rfloor+\frac{1}{\left\lfloor x_1\right\rfloor+\frac{1}{x_2}}=\left\lfloor x_0\right\rfloor+\frac{1}{\left\lfloor x_1\right\rfloor+\frac{1}{\left\lfloor x_2\right\rfloor+\frac{1}{x_3}}}=\cdots$$
We claim that this sequence is finite if and only if $x$ is rational. One direction follows immediately from the observation that $x_{i+1}$ is rational if and only if $x_i$ is rational. The other direction is also easy: If $x=\frac{p}{q}$, the above procedure is equivalent to the EUCLIDEAN ALGORITHM applied to $p$ and $q$. This also shows that for a given rational number $\frac{p}{q}$ with $p, q>0$ the (finite) sequence $x_1, x_2, \ldots, x_k$ as above can be computed in polynomial time. The following algorithm is almost identical to the EUCLIDEAN ALGORITHM except for the computation of the numbers $g_i$ and $h_i$; we shall prove that the sequence $\left(\frac{g_i}{h_i}\right)_{i \in \mathbb{N}}$ converges to $x$.

# 组合优化代考

## 数学代写|组合优化代写combinatoroptimization代考|线性规划算法

Simplex算法和ElLIPSOID METHOD的一个优点是它们不需要显式给出LP。有一个oracle(一个子例程)就足够了，它可以决定给定的向量是否可行，如果不可行，则返回违反的约束。我们将在第4.6节详细讨论椭球方法，因为它意味着许多组合优化问题可以在多项式时间内解决;对于某些问题，这实际上是唯一已知的证明多项式可解性的方法。这就是为什么我们在本书中只讨论椭球方法而不讨论内点算法的原因

## 数学代写|组合优化代写combinatoroptimization代考| continuing Fractions

. quot

(1)而$p>0$和$q>0$做:

(2) $\operatorname{Return} d:=\max {p, q}$ .

$$x=x_0=\left\lfloor x_0\right\rfloor+\frac{1}{x_1}=\left\lfloor x_0\right\rfloor+\frac{1}{\left\lfloor x_1\right\rfloor+\frac{1}{x_2}}=\left\lfloor x_0\right\rfloor+\frac{1}{\left\lfloor x_1\right\rfloor+\frac{1}{\left\lfloor x_2\right\rfloor+\frac{1}{x_3}}}=\cdots$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师