All Questions
Tagged with linearization binary-variable
25
questions
2
votes
1
answer
223
views
Set a limit on value change of a binary variable
I am working on an Energy Management problem. The objective is to minimize the electricity bill for the customer.
I have a time-series data with 15 min. intervals spanning the course of 1 year. The ...
2
votes
1
answer
216
views
How to transform a binary QP into an MILP?
I have a binary quadratic problem with objective ${\bf{x}}^T{\bf{Qx}}+{\bf{c}}^T{\bf{x}}$
subject to
${\bf{A}}{\bf{x}}\le{\bf{b}}$
${\bf{A}}_{eq}{\bf{x}}={\bf{b}}_{eq}$.
here ${\bf{x}}$ is binary.
...
- 2,377
1
vote
0
answers
74
views
How to linearize a product and ratio of $x$ and $y$ where $x$ is binary and $y$ is a continuous variable?
I am an electrical engineer who is currently learning about optimization. From this post, they have shown how to linearize the product of two binary variables.
But in my case, I have a product $x \...
2
votes
2
answers
96
views
How to linearize the product of a binary and a negative continuous variable?
Suppose we have a binary variable $x$ and a negative continuous variable $y$. How can we linearize the product $u=xy$?
- 31
0
votes
1
answer
186
views
Production scheduling
I'm formulating a scheduling problem with the following decision variables:
$$X_t \space \text{is power sold to market in time period t} \\
Y_t \space \text{is power used for production in time period ...
0
votes
0
answers
46
views
How to linearize such a constraint?
My original content was like this:
Assuming that server $k$ can only allocate corresponding computing functions to MU $i$ after receiving their tasks. Let
$$ y_{i,k,t} = \begin{cases} 1 & \text{if ...
- 11
3
votes
2
answers
396
views
How to model a binary variable?
I am trying to find a constraint for the following relationship, but am failing a bit at it right now. I want to find a linear constraint that does the following. The binary variable $switch_{ot}$ is ...
- 91
2
votes
3
answers
230
views
Linearization the product of three variables (two binary & one continuous)
Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$.
I am trying to model the following conditional equations as constraints:
\begin{cases}
...
- 113
3
votes
2
answers
302
views
Reformulate bilinear binary constraint
I'm a solving a model that has the following constraint:
$$
c_{p,n} = \sum_{s\in S}\sum_{i \in \{1,2,3\} } x_{p,s,i-1} x_{n,s,i}, \forall (p,n) \in C
$$
where both the $c$ and $x$ variables are binary,...
- 233
2
votes
1
answer
109
views
Expressing inner product of binary variables in MIP
I have a $m$ by $n$ matrix $X$ of binary variables in my MIP which represents a list of $m$ items each belonging to one of $n$ categories. $m$ is usually around $1,000$ while $n$ is much lower at ...
- 123
2
votes
1
answer
123
views
Linearize a product of binary variables with 2 indexes
I have the following inequality that I would want to linearize.
Consider that $r_{ij}, x_{ij}, y_{ij}$ are binary variables defined for every pair of nodes $(i,j) \in A$. Also, I have a set of nodes $...
2
votes
1
answer
138
views
Lifting a 3rd order polynomial into a higher dimensional space
An MINLP from a paper I am reading has the following expression in its constraints:
$$
p_{l,s}=z_lb_l\Delta\theta_{l,s}+b_l\lambda_{l,s}u_l\Delta\theta_{l,s}
$$
Where from left to right:
$p_{l,s}$: ...
- 113
3
votes
1
answer
177
views
How to deal with log0 in optimization problem
I am adding some constraints to my model described in my previous post, where a discontinuous piecewise-quadratic functions is the objective to be minimized in cvx.
Here I have an additional terms, ...
- 65
3
votes
1
answer
563
views
Constraints that set values to binary variables depending on other binaries
I am trying to write a mathematical problem that involves some conditions based on binary variables. More specifically, I have a set of three binary variables $d_1$, $d_2$, $d_3$ and depending on ...
- 133
2
votes
1
answer
2k
views
How to linearize the product of a binary and a continuous variable? [duplicate]
Suppose we have a binary variable $b \in \{0, 1\}$ and a continuous (possibly negative) variable $y \in \mathbb{R}$. How can we linearize the product $b \cdot y$?
- 1,572