# 数学代写|凸优化作业代写Convex Optimization代考|МАTH4071

#### 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 在代写凸优化Convex 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。我们的专家在代写凸优化Convex Optimization代写方面经验极为丰富，各种代写凸优化Convex 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
couryes™为您提供可以保分的包课服务

## 数学代写|凸优化作业代写Convex Optimization代考|Branch and Probability Bound Methods

For a single-objective optimization, branch and bound optimization methods are widely known. They are frequently based on the assumption that the objective function $f(\mathbf{x})$ satisfies the Lipschitz condition; see Section 4.2. These methods consist of several iterations, each includes the three following stages:

(i) branching of the optimization set into a tree of subsets,
(ii) making decisions about the prospectiveness of the subsets for further search, and
(iii) selection of the subsets that are recognized as prospective for further branching.
To make a decision at stage (8.5) prior information about $f(\mathbf{x})$ and values of $f(\mathbf{x})$ at some points in $\mathbf{A}$ are used, deterministic lower bounds (often called “underestimates”) for the infimum of $f(\mathbf{x})$ on the subsets of $\mathbf{A}$ are constructed, and those subsets $\mathbf{S} \subset \mathbf{A}$ are rejected for which the lower bound for $\mathrm{m}S=\inf {\mathbf{x c s}} f(\mathbf{x})$ does not exceed an upper bound $\hat{f}^$ for $\mathrm{m}=\min _{\mathbf{x} \in \mathbf{A}} f(\mathbf{x})$. (The minimum among evaluated values of $f(\mathbf{x})$ in $\mathbf{A}$ is a natural upper bound $\hat{f}^$ for $\mathrm{m}$.)

The branch and bound techniques are among the best deterministic techniques developed for single-objective global optimization. These techniques are naturally extensible to multi-objective case as shown in Chapter 5 . In the case of singleobjective optimization, deterministic branch and bound techniques have been generalized in [238] and [237] to the case where the bounds are stochastic rather than deterministic, and are constructed on the base of statistical inferences about the minimal value of the objective function. The corresponding methods are called branch and probability bound methods. In these methods, statistical procedures for testing the hypothesis $H_0: M_S \leq \hat{f}^*$ are applied to make a decision concerning the prospectiveness of a set $\mathbf{S} \subset \mathbf{A}$ at stage (ii). Rejection of the hypothesis $H_0$ corresponds to the decision that the global minimum $\mathrm{m}=\min _{\mathbf{x} \in \mathbf{A}} f(\mathbf{x})$ cannot be reached in $\mathbf{S}$. Unlike the deterministic decision rules such rejection may be false. This may result that the global maximizer is lost. However, an asymptotic level for the probability of the false rejection can be controlled and it will be fixed.

## 数学代写|凸优化作业代写Convex Optimization代考|Visualization

For the expensive black-box multi-objective optimization problems it seems reasonable to hybridize a computer aided algorithmic search with an interactive human heuristic. Visualization is very important in perception of relevant information by a human expert $[48,122,260,263]$. In this section we investigate possibilities of the visualization of scarce information on the Pareto front using a statistical model of the considered problem.
The following problem of bi-objective optimization is considered:
$$\min _{\mathbf{x} \in \mathbf{A}} \mathbf{f}(\mathbf{x}), \mathbf{f}(\mathbf{x})=\left(f_1(\mathbf{x}), f_2(\mathbf{x})\right)^T,$$
where the properties of $\mathbf{f}(\mathbf{x})$ and of the feasible region $\mathbf{A} \subseteq \mathbb{R}^d$ are specified later on. We are interested in the approximation and visualization of $\mathbf{P}(\mathbf{f})_O$ using scarce information obtained in the initial/exploration phase of optimization. The necessity of the exploration phase follows from the assumption on the black-box objectives. The human heuristic abilities can be advantageous here in perception of scarce information gained during the exploration. The restriction of information scarcity is implied by the assumption on expensiveness of the objectives. The further search can be rationally planned by the optimizer depending on the results of the exploration. Visualization is expected to aid the perception of the available results.
The exploratory phase assumes that we have values of the objective functions at some number of random points in $\mathbf{A}$ which are independent and uniformly distributed. This exploration method can be seen as an analog of a popular heuristic decision by throwing a coin in the case of a severe uncertain decision situation. Moreover. the uniform distribution of points in the feasible region is the worstcase optimal algorithm for the multi-objective optimization of Lipschitz objectives; see Chapter 6. Although in the latter case the uniformity is understood in the deterministic sense, the random uniform distribution of points is a frequently used simply implementable approximation of the deterministic one. Now we have to extract, nseful for the further search, information from the availahle data, i.e., from a set of $\mathbf{x}_i, \mathbf{y}_i=\mathbf{f}\left(\mathbf{x}_i\right), i=1, \ldots, n$.

In single-objective global optimization, some information on the global minimum of $f(\mathbf{x})$ can be elicited from the sample $z_i=f\left(\mathbf{x}_i\right)$, where $\mathbf{x}_i$ are independent random points, by means of the methods of statistics of extremes; see Section 4.4.

## 数学代写|凸优化作业代写Convex Optimization代考|Branch and Probability Bound Methods

(i) 将优化集分支成子集树，
(ii) 对子集的前瞻侏做出决策以进行进一步搜亰，以从及
(iii) 选择被认为具有进一步分支预期的子集。 估”）来表示 $f(\mathbf{x})$ 在子堆上 $\mathbf{A}$ 被构造，并且那些子集 $\mathbf{S} \subset \mathbf{A}$ 鿆拒绝的下限为
$m S=\inf x \operatorname{cs} f(\mathbf{x})$ 不超过上限 帞子 ${\mathrm{f}} \wedge$ 为了 $m=\min {\mathbf{x} \in \mathbf{A}} f(\mathbf{x})$. (评估值中的最小值 $f(\mathbf{x})$ 在 $\mathbf{A}$ 是目然上界 $、$ 帞子 ${f} \wedge \mathrm{s}} \mathrm{s}$ 为.) 分支定界技术是为单目标全局优化开发的最佳确定性技术之一。这些技术自然可以扩展到多 目标情况，如第 5 章所示。在单目标优化的情况下，确定性分支定界技术已在 [238] 和 [237] 中推广到边界是随机而不是确定性的情况，并且是基于关于目标函数。相应的方法称 为分支和概率界方法。在这些方法中，用于检验假设的统计程序 $H_0: M_S \leq \hat{f}^*$ 用于做出 关于集合的前瞻性的决定 $\mathbf{S} \subset \mathbf{A}$ 在阶段(ii)。拒绝假设 $H_0$ 对应于全局最小值的决定 $\mathrm{m}=\min {\mathbf{x} \in \mathbf{A}} f(\mathbf{x})$ 无法到达S. 与确定性决策规则不同，这种拒绝可能是错误的。这可能 导敖全局最大化器夆失。但是，可以控制错误拒绝概率的渐近水平并将其固定。

## 数学代写|凸优化作业代写Convex Optimization代考|Visualization

$$\min _{\mathbf{x} \in \mathbf{A}} \mathbf{f}(\mathbf{x}), \mathbf{f}(\mathbf{x})=\left(f_1(\mathbf{x}), f_2(\mathbf{x})\right)^T$$

## 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 :)