# Tag: optimization | 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
- ...

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...

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...

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...

Post #11
##### Optimization Learning Notes 5

book Public Date: 2020-07-08 05:11:21.020777

update Update Date: 2020-08-08 01:55:03.360573

From this note, we will start talk about non-linear programs. To get a first glance of NLPs, let us first check out how we can issue the Interior Point Method.
Interior Point Method
Interior Point Method takes care of the primal and the dual problem at the...