# 计算机代写|计算机视觉代写Computer Vision代考|CS231n Characteristics of Optimization Problems

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## 计算机代写|计算机视觉代写Computer Vision代考|Characteristics of Optimization Problems

Optimization plays an important role in computer vision, because many computer vision algorithms employ an optimization step at some point of their proceeding. Before taking a closer look at the diverse optimization methods and their utilization in computer vision, let’s first clarify the concept of optimization. Intuitively, in optimization we have to find a solution for a given problem which is “best” in the sense of a certain criterion.

Consider a satnav system, for example: here the satnav has to find the “best” route to a destination location. In order to rate alternative solutions and eventually find out which solution is “best,” a suitable criterion has to be applied. A reasonable criterion could be the length of the routes. We then would expect the optimization algorithm to select the route of shortest length as a solution. Observe, however, that other criteria are possible, which might lead to different “optimal” solutions, e.g., the time it takes to travel the route leading to the fastest route as a solution.

Mathematically speaking, optimization can be described as follows: Given a function $f: S \rightarrow \mathbb{R}$ which is called the objective function, find the argument $x^$ which minimizes $f$ : $$x^=\underset{x \in S}{\arg \min } f(x)$$
$S$ defines the so-called solution set, which is the set of all possible solutions for our optimization problem. Sometimes, the unknown(s) $x$ are referred to design variables. The function $f$ describes the optimization criterion, i.e., enables us to calculate a quantity which indicates the “goodness” of a particular $x$.

## 计算机代写|计算机视觉代写Computer Vision代考|Categorization of Optimization Problems

Optimization methods are widely used in numerous computer vision applications of quite diverse nature. As a consequence, the optimization methods which are best suited for a certain application are of quite different nature themselves. However, the optimization methods can be categorized according to their properties. One popular categorization is according to the nature of the solution set $S$ (see e.g. [7]), which will be detailed below.

We talk about continuous optimization if the solution set $S$ is a continuous subset of $\mathbb{R}^n$. Typically, this can be a bounded region of $\mathbb{R}^n$, such as a subpixel position $[x, y]$ in a camera image (which is bounded by the image width $W$ and height $H:[x, y]$ $\in[0, \ldots, W-1] \times[0, \ldots, H-1])$ or an $m$-dimensional subspace of $\mathbb{R}^n$ where $m$ (e.g., a two-dimensional surface of a three-dimensional space – the surface of an object). Here, the bounds or the subspace concept acts as constraints, and these are two examples why continuous optimization methods often have to consider constraints.

A representative application of continuous optimization is regression, where observed data shall be approximated by functional relationship. Consider the problem of finding a line that fits to some measured data points $\left[x_i, y_i\right]$ in a two-dimensional space (see Fig. 1.1). The line $l$ to be found can be expressed through the functional relationship $l: y=m x+t$. Hence, the problem is to find the parameters $m$ and $t$ of the function. A criterion for the goodness of a particular fit is how close the measured data points are located with respect to the line. Hence, a natural choice for the objective function is a measure of the overall squared distance:
$$f_l(\mathbf{x})=\sum_i\left|y_i-\left(m \cdot x_i+t\right)\right|^2$$

$\$$S 定义了所调的解集，它是我们优化问题的所有可能解的集合。有时候，末知的 s x 被称为设计变量。功能 f 描述了优化标准，即，使我们能够计算一个数量，该数 量表明一个特定的“好” x. ## 计算机代写|计算机视觉代写COMPUTER VISION代 考|CATEGORIZATION OF OPTIMIZATION PROBLEMS 优化方法广泛用于许多性质各异的计算机视觉应用中。因此，最适合特定应用的优化方法本身具有完全不同的性质。然而，优化方法可以根据它们的特性进行分 类。一种流行的分类是根据解决方安集的性质.S seee. g .[7],下面会详细介绍。 如果解决方安集我们谈论持续优化 S 是一个连续子集 \mathbb{R}^n. 通常，这可以是一个有界区域 \mathbb{R}^n ，比如一个子像俦位置 [x, y] 在相机图像中 whichisboundedbytheimagewidth \ W \andheight \ H:[x, y] \ \ \in[0, \ldots, W-1] \times[0, \ldots, H-1] oran米-dimensionalsubspaceof \backslash mathbb {\mathrm{R}] \wedge \mathrm{n} where 美元e.g., atwo – dimensionalsurfaceofathree – dimensionalspace-thesurfaceofanobject. 在这里，边界或子空间概念充当约束，这是连续优化方法 经常必须考虑约束的两个例子。 连续优化的一个代表性应用是回归，其中观䕓到的数据应通过函数关系近似。考慮找到适合某些测量数据点的线的问题 \left[x_i, y_i\right] 在二维空间 s e e F i g .1 .1. 线 l 可以通 过函数关系来表示 l: y=m x+t. 因此，问题是找到参数 m 和 t 的功能。特定拟合优度的标准是测量数据点相对于线的位置有多接近。因此，目标函数的自然选择 是总平方距离的度量:$$ f_l(\mathbf{x})=\sum_i\left|y_i-\left(m \cdot x_i+t\right)\right|^2$\$
Optimization problem classification

## 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。