Statistics-lab™可以为您提供uio.no MAT3100 Linear Programming线性规划课程的代写代考和辅导服务！

MAT3100 Linear Programming课程简介

The book is a comprehensive text on linear programming, covering both the theoretical foundations and practical applications of the subject. It is intended for graduate-level students and researchers in mathematics, engineering, and related fields.

Some of the topics covered in the book include linear algebra, convex analysis, duality theory, sensitivity analysis, and algorithms for solving linear programming problems. The book also includes numerous examples and exercises to help readers develop their understanding of the material.

If you have access to SpringerLink through your institution, you should be able to access the book online. You can search for the book on the SpringerLink website and click on the “Access” button to log in and view the book.

PREREQUISITES 

Instructor: Mikhail Lavrov
Location: Mathematics 112
Lecture times: 5:00pm to 6:15pm on Tuesday and Thursday
Textbook: Linear Programming: Foundations and Extensions by Robert
Vanderbei. You can access it online via SpringerLink (you will have to click Log in, in the top right, and access it via KSU’s subscription).
Office hours: Tuesday 12:00pm to 1:00pm, Wednesday 4:00pm to 5:00pm in Mathematics 245.
D2L page: https://kennesaw.view.usg.edu/d2l/home/2672229
During the scheduled office hours, you are welcome to stop by my office without an appointment: answering your questions is the reason I’m there! Outside that time, please email me at [email protected] and I will either answer your question by email, or we will find a different time to meet.
(However, it is difficult for me to adjust my schedule on very short notice, so please email me the day before if you want to set up a meeting.)

D2L will be used to submit assignments (these will be posted both here and on D2L, for convenience) and to view grades. The syllabus is also posted on D2L.

MAT3100 Linear Programming HELP（EXAM HELP， ONLINE TUTOR）

Proof If $f$ has no relative minima the theorem is valid by default. Assume now that $c_0$ is the minimum of $f$. Then clearly $\Gamma=\left{\mathbf{x}: f(\mathbf{x}) \leqslant c_0, \mathbf{x} \in \Omega\right}$ and this is convex by Proposition 3 of the last section.

Suppose now that $\mathbf{x}^* \in \Omega$ is a relative minimum point of $f$, but that there is another point $\mathbf{y} \in \Omega$ with $f(\mathbf{y})<f\left(\mathbf{x}^\right)$. On the line $\alpha \mathbf{y}+(1-\alpha) \mathbf{x}^, 0<\alpha<1$ we have
$$
f\left(\alpha \mathbf{y}+(1-\alpha) \mathbf{x}^\right) \leqslant \alpha f(\mathbf{y})+(1-\alpha) f\left(\mathbf{x}^\right)<f\left(\mathbf{x}^\right), $$ contradicting the fact that $\mathbf{x}^$ is a relative minimum point.
We might paraphrase the above theorem as saying that for convex functions, all minimum points are located together (in a convex set) and all relative minima are global minima. The next theorem says that if $f$ is continuously differentiable and convex, then satisfaction of the first-order necessary conditions are both necessary and sufficient for a point to be a global minimizing point.

Proof We note parenthetically that since $\mathbf{y}-\mathbf{x}^$ is a feasible direction at $\mathbf{x}^$, the given condition is equivalent to the first-order necessary condition stated in Sect. 7.1. The proof of the proposition is immediate, since by Proposition 4 of the last section
$$
f(\mathbf{y}) \geqslant f\left(\mathbf{x}^\right)+\nabla f\left(\mathbf{x}^\right)\left(\mathbf{y}-\mathbf{x}^\right) \geqslant f\left(\mathbf{x}^\right)
$$
Next we turn to the question of maximizing a convex function over a convex set. There is, however, no analog of Theorem 1 for maximization; indeed, the tendency is for the occurrence of numerous nonglobal relative maximum points. Nevertheless, it is possible to prove one important result. It is not used in subsequent chapters, but it is useful for some areas of optimization (Fig. 7.5).

Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.

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