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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
 - ...
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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 ...
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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...
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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...
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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...
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