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
- ...
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
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...Read More Raw Content