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