Questions tagged [linearization]
For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.
259
questions
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Better formulation of bilinear terms
I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
- 23
2
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1
answer
251
views
Replace the constraint using ==> by a linear formulation
I would like to know how to express the continuity constraint without using a decision variable in the conditional form. My challenge is to stay with a linear formulation.
I will start to explain my ...
1
vote
1
answer
141
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How do I linearize such a constraint?
I was wondering, how one would linearize such a constraint, to make it applicable to LPs.
$ a_{i}=(a_{i-1}+b_{i})(1-c_{i})-d_{i}$
$a_i$ gives information of the number of assigned jobs to machine $i$. ...
2
votes
1
answer
96
views
How to transfer an objective with separate positive and negative parts into linear programming
I've got to deal with an optimization problem as follows,
$$
\begin{aligned}
\max_{x,y} & a^Tx+y^TKx\\
{s.t.}&Ax=b\\
&{Cx}\leq d\\
l&\leq y\leq u\end{aligned}
$$
where $x \in \bf{R}^n$,...
4
votes
1
answer
328
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Optimization problem with the Harmonic number
I have an optimization problem:
\begin{align*}
\text{ minimize } \sum_{i=1}^n H(x_i)
\\
\text{ subject to } Ax \geq b, x\geq 0, x\in \mathbb{Z}^n
\end{align*}
where $H(n)$ is the $n$-th Harmonic ...
- 1,015
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answers
31
views
Moment based linearization of PDF for LP based optimization
Suppose I’m interested in modeling risk/volatility using the Cauchy distribution and I’d like to optimize some allocations using linear programming.
The Cauchy distribution is quadratic in nature but ...
- 551
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65
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transform minimize weighted sum of absolute value into a linear optimization
For example, we have an optimization problem
$$
\min \sum_{i=1}^{n} |w_{i} - a_{i}| b_{i} \quad \text{s.t.} \quad \sum_{i=1}^{n} c_i w_i = 0
$$
and $a_i, b_i, c_i$ are given. How to convert it into a ...
- 11
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74
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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
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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
1
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125
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How to linearize the following constraints
Given the following two expressions:
$ x - \frac{1}{T}\sum_{i} y_{i}$
$ x - \frac{1}{Q}\sum_{i} \beta_{i} y_{i}$
where $x \in \mathbb{Z}_{+}$, $y \in \mathbb{R}_{+}$, and $T$, $Q$ and $\beta_{i}$ ...
- 113
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186
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Production scheduling
I'm formulating a scheduling problem with the following decision variables:
$$X_t \space \text{is power sold to market in time period t} \\
Y_t \space \text{is power used for production in time period ...
3
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124
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From Quadratic to MILP?
I am playing around with some Quadratic Programs (QPs), and I want to check if my reasoning is right concerning a re-modeling from QP to MILP. So, let's consider the below QP:
(QP) $\min c^T x + x^T Q ...
- 1,240
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64
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how to linearize if-then when having an operand?
if $x_{i,j,p,s}$ and $y_{i,j,p,s}$ are binary and $z_i^s$ is integer; how to enforce:
$$
((x_{i,j,p,s}=1) \land (z_i^s \ge 5 )) \implies y_{i,j,p,s}=1
$$
The value of $z$ in my problem could be 1 to ...
- 33
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157
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Matrix lookup modelling variants
As part of a bigger model I have a matrix of variables $x_{ij} \geq 0$ and a "selector" set of variables $y_j \in \{0,1\}, \sum_j y_j = 1$.
From $x_{ij}$ I'd like to get the variables of ...
- 113
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88
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Handling Variable Division in CVXPY for Calculating Annualized Rate of Change
I am working with a dataset that contains multiple entries for different IDs across various years. Some IDs might have a gap of years between entries. My goal is to solve an optimization problem using ...
- 111