# Tag: math | Page 0

Post #2

##### Optimization Learning Notes 1

*book*
Public Date: 2020-06-20 08:42:04.801901

*update*
Update Date: 2020-07-30 15:33:51.919974

Modeling Mathematically, an optimization problem is usually represented as: $$ \begin{aligned} \text{maximize/minimize}_x &~ f(x) \ \text{subject to} &~ x \in \Omega \end{aligned} $$ where: - $x$ is the decision variable - $f$ is the objective function - ...Read More Raw Content

Post #5

##### Introduction to Category Theory 1

*book*
Public Date: 2020-06-17 10:48:50.306174

*update*
Update Date: 2020-06-21 04:11:27.547781

What is a Category? A category $C$ consists of - a collection $Obj$ of entities called objects - a collection $Arw$ of entities called arrows - three assignments: - source: $Arw \to Obj$ - target: $Arw \to Obj$ - id: $Obj \to Arw$ - a partial ...Read More Raw Content

Post #6

##### Optimization Learning Notes 2

*book*
Public Date: 2020-06-20 17:12:00.571290

*update*
Update Date: 2020-07-30 15:34:13.181702

Recall that the standard of an LP is like the following: $$ \begin{aligned} \min &~~~ c^Tx \ \text{subject to} &~~~ Ax = b \ &~~~ x \ge 0 \end{aligned} $$ where $x \in \mathbb R^n, b \in \mathbb R^m, A \in \mathbb R^{m\times n}$ In the following discussio...Read More Raw Content

Post #8

##### Optimization Learning Notes 3

*book*
Public Date: 2020-06-24 11:49:25.724151

*update*
Update Date: 2020-07-30 15:34:37.990602

Two-Phase Method with Simplex Tableau TL;DR, two-phase method involves two LP and can be solved by construct two simplex tableau. However, there two things to consider: - How to acquire the initial tableau in Phase I. - How to make the transition from Ph...Read More Raw Content

Post #10

##### Optimization Learning Notes 4

*book*
Public Date: 2020-07-02 15:02:38.926921

*update*
Update Date: 2020-07-30 15:35:06.065394

Interpreting the Dual Problem It turns out that dual problem actually have their own meanings. The interpretations of dual problems may give us a better understanding of the duality theory. Production Planning Production Planning problem is one of the most...Read More Raw Content