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

## 数学代写|凸优化作业代写Convex Optimization代考|Multidimensional Bi-objective Lipschitz Optimization

The problem of bi-objective non-convex optimization
$$\min _{\mathbf{x} \in \mathbf{A}} \mathbf{f}(\mathbf{x}), \mathbf{f}(\mathbf{x})=\left(f_1(\mathbf{x}), f_2(\mathbf{x})\right)^T, \mathbf{A} \subset \mathbb{R}^d,$$
is considered, where the properties of the objective functions and the feasible region will be defined later.

The construction of an optimal algorithm in a broad class of global optimization algorithms is difficult [239]; nevertheless some partially optimal solutions usually are possible. We assume that the feasible region is a hyper-rectangle $\mathbf{A}=\left{x: a_i \leq\right.$ $\left.x_i \leq b_i, i=1, \ldots, d\right}$, and the objective functions are Lipschitz continuous. In the present section we consider hybridization of the branch and bound approach and the concept of one-step worst-case optimality with respect to the class of Lipschitz functions. Multi-objective branch and bound is presented in Chapter 5, and for the thorough presentation of branch and bound in global (including multi-objective) optimization we refer to $[55,87,185,208]$, and for the arguments in favor of the Lipschitz model we refer to $[87,110,159,168,196]$.

We analyze the possibility to generalize, for the multidimensional case, the results of Section 6.2.4 concerning the univariate $(d=1)$ bi-objective optimization. The arguments in Section 6.2.4 show that in the worst-case setting the concept of sequential one-step optimality seems most appropriate from the applications point of view. To generalize a univariate algorithm for the multidimensional case we apply hyper-rectangular partitioning with diagonal approach [259]. The feasible region is sequentially partitioned into decreasing hyper-rectangles which are selected for subdivision on the base of a criterion which depends on the objective function values at the endpoints of the diagonal. Our goal is to define a criterion of the selection and the rule of the bisection according to the concept of one-step worst-case optimality. Besides of the one-step optimal (bisection) algorithm a similar trisection algorithm is developed where hyper-rectangles covering the feasible region are subdivided into three equal parts [259].

## 数学代写|凸优化作业代写Convex Optimization代考|Lipschitz Bound for the Pareto Frontier

In this section we consider Lipschitz continuous functions for which the city-block metric is used in the decision space, i.e., the following inequalities are valid:
$$\left|f_k(\mathbf{x})-f_k(\mathbf{z})\right| \leq L_k \cdot \sum_{i=1}^d\left|x_i-z_i\right|, k=1,2,$$

where $\mathbf{x} \in \mathbf{A}, \mathbf{z} \in \mathbf{A}, L_k>0, k=1,2$
The class of Lipschitz continuous functions is advantageous for constructing global minimization algorithms because of relatively simply computable lower bounds for the function values. The availability of such bounds enables a theoretical assessment of the quality of a discrete representation of the Pareto front for biobjective Lipschitz optimization.

## 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