What are the prerequisites in general to study mathematical Programming \ Optimization?

Question

What are the prerequisites in general to study mathematical Programming \ Optimization? I'm new to this theory. Please Provide me with detailed Answers.

Answer 1

The knowledge of Linear algebra and analysis in space $ \mathbb {R}^n $ is fundamental. Just to get you started you need to know

1. Understanding the difference between local theorem and global theorem in Analysis.

2. Understand the derivative $Df:\mathbb{R}^n\to \mathbb{R}^m$ of a function $f:U\subset\mathbb{R}^n\to\mathbb{R}^m$ as the best linear (local) approximation of the function.

3. Understand that the derivative $Df(x): \mathbb{R}^n\to \mathbb{R}^m$ of a function $f:U\subset\mathbb{R}^n\to \mathbb{R}^m$ is a linear transformation.

4. Bolzano–Weierstrass theorem for sequences in $\mathbb{R}^n$

5. Extreme value theorem for functions $f:U\subset\mathbb{R}^n\to\mathbb{R}$

6. Convex functions $f:U\subset \mathbb{R}^n\to\mathbb{R}$ for $U$ convex
7. Taylor's expansion theorem for $C^2$ functions $f:U\subset\mathbb{R}^n\to\mathbb{R}$
8. It is important to understand the proof of the Lagrange multiplier theorem that is done using the implicit function theorem.

If you want to start studying I suggest you start with the Nonlinear Programming by Dimitri Bertsekas.