MY-ASSIGNMENTEXPERT™可以为您提供wgtn.ac EEEN422 Convex Optimization凸优化课程的代写代考和辅导服务！
这是惠灵顿维多利亚大学凸优化课程的代写成功案例。
EEEN422课程简介
Convex Optimisation
Convex optimisation problems are common in science, engineering and economics. The course teaches identifying and solving convex optimisation problems. It discusses convex sets and functions, linear and quadratic programs, semi-definite programming, and duality theory. It uses these concepts to solve practical optimisation problems .
Students who pass this course should be able to:
- Demonstrate an understanding of the fundamental concepts of convex optimization such as convexity, linear, quadratic and semi-definite programs, and duality theory.
- Recognize and formulate convex optimization problems.
- Solve convex optimization problems by selecting and implementing suitable algorithms.
- Use standard software package(s) for solving convex optimization problems.
Prerequisites
2022: The course is primarily offered in-person, and there are components such as tests, labs, tutorials, and marking sessions which require in-person attendance. There will be remote alternatives for all the components of the course, but these are only available to students studying from outside the Wellington region. The remote option for tests will use a Zoom-based system for online supervision of the tests.
Students taking this course remotely must have access to a computer with camera and microphone and a reliable high speed internet connection that will support real-time video plus audio connections and screen sharing. Students must be able to use Zoom; other communication applications may also be used. A mobile phone connection only is not considered sufficient. The comuputer must be adequate to support the programming required by the course: almost any modern windows, macintosh, or unix laptop or desktop computer will be sufficient, but an Android or IOS tablet will not.
EEEN422 Convex Optimization HELP（EXAM HELP， ONLINE TUTOR）
Consider the support vector machine (SVM) classification problem discussed in class. Given labeled dataset $\left{x^i, y^i\right}_{i \in[N]}$ where each $x^i \in \mathbf{R}^n$ is associated with a label $y^i \in{1,-1}$ such that $y^i=1$ if $x^i \in A$ and $y^i=-1$ if $x^i \in B$. Consider the following classification problem with soft margin:
$$
\begin{array}{rlr}
\min {w \in \mathbb{R}^n, b \in \mathbb{R}, \epsilon \in \mathbb{R}^N} & \frac{1}{2}|w|_2^2+C \sum{i=1}^N \epsilon_i & \
\text { s.t. } & 1-y^i\left(w^{\top} x^i+b\right) \leq \epsilon_i, \quad \forall i \in[N], \
& \epsilon_i \geq 0, \quad \forall i \in[N] . &
\end{array}
$$
Show that the dual of the above problem is given by:
$$
\begin{aligned}
\min {\lambda \in \mathbb{R}^N} & -\frac{1}{2} \sum{i=1}^N \sum_{j=1}^N \lambda_i \lambda_j y^i y^i\left(x^i\right)^{\top} x^j+\sum_{i=1}^N \lambda_i \
\text { s.t. } & 0 \leq \lambda_i \leq C, \quad \forall i \in[N] \
& \sum_{i=1}^N \lambda_i y^i=0 .
\end{aligned}
$$
Given the optimal dual solution $\lambda^$, find the optimal primal solution $w^$ and $b^*$.
Show that the Support Vector Classification problem can be stated equivalently as:
$$
\min {w \in \mathbb{R}^n, b \in \mathbb{R}} \lambda|w|_2^2+\frac{1}{N} \sum{i=1}^N \max \left(0,1-y^i\left(w^{\top} x^i+b\right)\right) .
$$
How does $\lambda$ relate with $C$ in the previous formulation?
Given dataset $\left{x^i, y^i\right}_{i \in[N]}$ where each $x^i \in \mathbf{R}^n$ and $y^i \in \mathbb{R}$ and linear hypothesis $f(x)=w^{\top} x+b$, the $\epsilon$-support vector regression problem is given by
$$
\begin{array}{rlr}
\min _{w \in \mathbb{R}^n, b \in \mathbb{R}} & \frac{1}{2}|w|_2^2 & \
\text { s.t. } & y^i \leq w^{\top} x^i+b+\epsilon, & \forall i \in[N], \
& y^i \geq w^{\top} x^i+b-\epsilon, & \forall i \in[N] .
\end{array}
$$
Find the dual of the above problem and show how to derive the primal optimal solution from the dual optimal solution.
Let $C_1=\left{x \in \mathbb{R}^2 \mid x_1 \geq 0, x_2 \geq 0\right}$, and let $C_2=\left{x \in \mathbb{R}^2 \mid x_1 \leq 0, x_2 \leq 0\right}$. Find a hyperplane that separates $C_1$ and $C_2$.
MY-ASSIGNMENTEXPERT™可以为您提供WGTN.AC EEEN422 CONVEX OPTIMIZATION凸优化课程的代写代考和辅导服务！
