MY-ASSIGNMENTEXPERT™可以为您提供stanford.edu MS&E310 Linear Programming线性规划课程的代写代考和辅导服务！
这是斯坦福大学 线性规划课程的代写成功案例。
MS&E310课程简介
Topics include: Problem formulation of standard (conic) linear programming models, the theory of polyhedral and conic convex sets, linear inequalities, alternative theorems and duality, sensitivity analyses and economic interpretations, and relaxations of harder optimization problems. Algorithms include the simplex method, interior-point methods, and ADMM and other (first-order) iterative methods. Complexity and/or computation efficiency analysis for linear programming. Applications include dynamic resource allocation, on-line mechanism design, algorithmic game-theory, SVM/data-classification, and MDP/reinforced learning.
Prerequisites
The field of optimization is concerned with the study of maximization and minimization of mathematical functions. Very often the arguments of (i.e., variables in) these functions are subject to side conditions or constraints. By virtue of its great utility in such diverse areas as applied science, engineering, economics, finance, medicine, and statistics, optimization holds an important place in the practical world and the scientific world. Indeed, as far back as the Eighteenth Century, the famous Swiss mathematician and physicist Leonhard Euler (1707-1783) proclaimed that … nothing at all takes place in the Universe in which some rule of maximum or minimum does not appear. The subject is so pervasive that we even find some optimization terms in our everyday language.
MS&E310 Linear Programming HELP（EXAM HELP， ONLINE TUTOR）
Let $G$ be a graph where every edge has a different weight (as we assumed in class). Show that the edge with the smallest edge weight overall is in the minimum spanning tree.
Let $G$ be a graph of $n$ nodes where every edge weight is either 1 or 2 (now edges can have the same weight). Let $G^{\prime}$ be $G$ with edges of weight 2 removed. Show that the weight of the minimum spanning tree of $G$ is $n-2+\operatorname{cc}\left(G^{\prime}\right)$, where $\operatorname{cc}\left(G^{\prime}\right)$ is the number of connected components of $G^{\prime}$.
Let $G$ be a graph with positive, integer edge weights where several edges may have the same weights. Show that, for all integers $i$, the number of edges of weight $i$ is the same in every minimum spanning tree of $G$.
You are given an undirected graph $G=(V, E)$ with edge weights $d(u, v)$, which you can assume are all distinct, and you are given a minimum spanning tree $T$ on $G$. You expect one of the edges of $G$ to disappear at some time in the future, but you don’t know which edge it will be, and when the edge does disappear, you’ll need to find another minimum spanning tree very quickly. For example, the MST represents a communication network for stock traders, and if a link fails, you have to fix it as fast as possible.
Give an efficient algorithm to preprocess $T$ and $G$ to label each edge $e$ in $T$ with another edge $r(e)$ of $G$ so that if $e$ disappears, adding $r(e)$ to the tree creates a new minimum spanning tree in the modified graph.
Let $G$ be a graph where every edge has a different weight (as we assumed in class). Show that there is only one, unique minimum spanning tree in this case.
MY-ASSIGNMENTEXPERT™可以为您提供STANFORD.EDU MS&E310 LINEAR PROGRAMMING线性规划课程的代写代考和辅导服务！
