Skip to main content

Questions tagged [linearization]

For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.

Filter by
Sorted by
Tagged with
2 votes
1 answer
114 views

Priority based demand fulfilment in Linear Constraint

Say I have 3 sources. D1, D2, D3. their capacity is 100, 200, 400. I want to create some constraints such that First D1 is depleted then D2 and then D3. But the catch is you cant use min or max ...
kunal chakraborty's user avatar
2 votes
1 answer
109 views

How to model the constraints of min and max in cvxpy

I have a continuous variable $x_{ij}\in[0,1]$ and I need to write the following constraint: $$M_i-m_i+1\leq C_i$$ where $M_i=\max\{j: x_{ij}>0\}$ and $m_i=\min\{j: x_{ij}>0\}$
zdm's user avatar
  • 403
4 votes
2 answers
295 views

Linear condition between two continuous variables

There are two real variables $x$ and $y$. The conditions are such that: if $y\le 0$, then $x=0$ if $y>0$, then $x=y$ How to write linear equations or inequalities to satisfy both the conditions?
Lorentz's user avatar
  • 41
0 votes
1 answer
104 views

How to model this constraint in a better way?

I have a resource allocation problem. There are $M$ users and $N$ resources (machines). One user can be assigned to multiple resources/machines. But maximum $B$ machines can be activated at a time for ...
KGM's user avatar
  • 2,297
3 votes
1 answer
191 views

Reformulate constraints

I have the following constraints and am wondering whether I can formulate the whole thing more narrowly and with fewer constraints. $x_{itk}$ is binary and $u_{it}, v_{itk}\in [0,1]$. $M$ is a Big-M ...
manofthousandnames's user avatar
0 votes
0 answers
40 views

Linearizing a continuous function

is there a way to linearize this and plug it in a mathematical model ? Suppose I have a continuous variable, if used once, it triggers a secondary effect that reduces the targeted upper bound by a ...
applethal's user avatar
2 votes
1 answer
79 views

Is the linearization with first-order Taylor approximation correct?

I have a QP problem as $\min \hspace{2mm} x^TQx-c^Tx$ here $x$ in binary I want to transform it into a MILP by writing the objective function as $\min \hspace{2mm} z-c^Tx$ and then adding a constraint ...
KGM's user avatar
  • 2,297
1 vote
1 answer
45 views

Converting a function composing of multipe pieces into a linear equation

I have a variable (alpha) which depends on some other binary variables, denoted as X_i. So, for some combination of other variables, alpha may take a value (Beta_j). I added some auxillary variables (...
Sam's user avatar
  • 97
0 votes
1 answer
36 views

Add second "constraint" to model a binary variable

in my model I have the binary variable $f_{ij}$ which pushes a time-dependent $j$ integer variable $D_{ij}$ to zero if $f_{ij}$ takes the value 1 and keeps the integer number if $f_{ij}$ equals 0. Yes,...
marvelfab12's user avatar
1 vote
1 answer
82 views

How to model $\max\limits_{x\in X} \min\limits_{y\in Y} \max\limits_{z\in Z} f(z)$ as single MILP

I have the following optimization problem: \begin{align*} \max\limits_{x\in X} &\min\limits_{y\in Y} \max\limits_{z\in Z} & f(z) \\ &\text{such that} & (x, y, z)\in P \end{align*} ...
graphtheory123's user avatar
0 votes
0 answers
64 views

Is it possible to transform MIQP into MILP without introducing new variable?

I have a QP optimization problem in the form $$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$ here $\bf Q$ is a symmetric matrix. $\bf x$ is the optimization variable, and it is binary. Is there a way to ...
KGM's user avatar
  • 2,297
0 votes
2 answers
85 views

linearizing a constraint involving an absolute function

I would like to know what is the best way to linearize a constraint involving an absolute function. More precisely, imagine I have three binary variables and their relationships is as follows: |x-y| = ...
Sam's user avatar
  • 97
1 vote
1 answer
64 views

Linearizing a quadratic constraint

I am working on a quadratic conic optimization problem, but I have discovered that it would be preferable if the quadratic constraint is linearly approximated. In other words, I need some way to make ...
Mikkel Honningsvåg Sandhaug's user avatar
0 votes
1 answer
55 views

How to linearize this L0 norm of a vector?

I have an QP optimization problem. $\bf x$ is the binary optimizaion variable of size $12\times 1$. One of the constraints is non-linear/non-convex. The constraint is L0 constraint. The constraint I ...
KGM's user avatar
  • 2,297
2 votes
1 answer
212 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. ...
KGM's user avatar
  • 2,297
0 votes
0 answers
116 views

why this little constraint changes my whole program?

I'm trying to linearize a CP in ILOG CPLEX. I have the following constraint that I want to linearize (I already simplified it with the big M) : ...
Marcocorico's user avatar
0 votes
0 answers
66 views

Why are these two constraint equations not equivalent?

I've made a CP Model of an hospital in ILOG CPLEX and I want to test the performance of the CPLEX version of it. In my CP model, I have the following constraint : ...
Marcocorico's user avatar
0 votes
2 answers
121 views

Converting a piecewise function to linear equations

I am trying to build a MILP model. In this model, I have a dependent variable (alpha) that its value depends on the value of some other variables (or different combination of some other variables). In ...
Sam's user avatar
  • 97
-1 votes
1 answer
66 views

How to linearize a product of an integer and a binary variable

i have this constraint right here, which is not linear. How would i linearize such a product. $number_t$ is a positive integer and $new_t$ and $reset_t$ are binary. $$number_t = (number_{t-1}+new_t)\...
Uni ewr's user avatar
  • 61
1 vote
1 answer
109 views

Convex approximation of a constraint

I have a constraint given as $ \left|x_n+\beta x_{n+ 1}\right|-\varepsilon_{ky}\left|x_{n}\right|\leq0\hspace{1em}\forall n=1,2...,N $ I need to convert this into a convex form to implement in CVX. $...
Muhammad's user avatar
0 votes
1 answer
64 views

Formulation of a stepwise linear approximation

I am currently trying to solve an MILP in Gurobi. Unfortunately, Gurobi does not support non-linear functions and I would like to do the following. I currently have the following constraint. It ...
nflgreaternba's user avatar
3 votes
2 answers
225 views

Convex equivalent of a constraint

I have a constraint as follows in my MILP model: $$ \sum_{e} (a_1(e) - a_2(e))^2 \leq M $$ Where, $a_1(e)$ and $a_2(e)$ are binary variables. Would you please guide me how can I find the equivalent ...
Mohammad Reza Salehizadeh's user avatar
0 votes
1 answer
85 views

How to represent "if $y_{it} = 1$ and $z_{jt'}=1$ then $x_{ij,t+t'}=1$"

There is a fulfillment problem in the e-commerce logistics field, where the fulfillment of each order is composed of a main transport (from City A to City B, referred to as a route) and an end ...
Ying's user avatar
  • 105
0 votes
0 answers
54 views

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 ...
Lemma's user avatar
  • 23
2 votes
1 answer
250 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 ...
Basma Ben Mahmoud's user avatar
1 vote
1 answer
132 views

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 $i$. ...
manofthousandnames's user avatar
2 votes
1 answer
95 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 $x \in \bf{R}^n$,...
Kaiming Zhang's user avatar
4 votes
1 answer
322 views

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 ...
Erel Segal-Halevi's user avatar
1 vote
0 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 ...
jbuddy_13's user avatar
  • 551
1 vote
0 answers
61 views

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 ...
Pique's user avatar
  • 11
1 vote
0 answers
55 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 \...
Tuong Nguyen Minh's user avatar
2 votes
2 answers
93 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 $u=xy$?
m.amin's user avatar
  • 31
1 vote
1 answer
122 views

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 $\beta_{i}$ ...
CHE's user avatar
  • 113
0 votes
1 answer
172 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 ...
fikacoder's user avatar
3 votes
0 answers
120 views

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 ...
Matheus Diógenes Andrade's user avatar
2 votes
1 answer
64 views

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 ...
Hemfri's user avatar
  • 33
1 vote
2 answers
157 views

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 ...
Christian's user avatar
  • 113
1 vote
0 answers
68 views

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 ...
user760900's user avatar
1 vote
1 answer
51 views

How to linearize stepped pricing in a route assignment problem

There is an allocation problem, while we have to assign logistics routes to multiple candidate carriers. For simplicity, let's assume there are only two routes, $A$ and $B$, with two candidate ...
Ying's user avatar
  • 105
1 vote
1 answer
434 views

Is it possible to do a linearization without introducing new variables?

I have three binary variables $x_{i,j}^{m,r}$ , $y_i^{m,r}$, and $z_i^{m,r}$. There is another integer variable $w_i^r$. And I want to linearize the following logic: $$ \sum_{m} x_{i,j}^{m,r} \ge 1 \...
Rainbow's user avatar
  • 53
0 votes
1 answer
128 views

applying a piecewise linearized equation in pulp

The background is I'm building a toy rent vs. buy mortgage calculator. I am an experienced software engineer but my math skills are 20 years behind me and I admit to being very lost. I've been using ...
kashahkashah's user avatar
1 vote
2 answers
215 views

Linearizing if else conditions in ILP

We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that, a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} =...
ephemeral's user avatar
  • 917
0 votes
0 answers
94 views

Transforming a quadratic constraint into a linear constraint

I have a problem with a quadratic constraint and I want to transform it into a linear constraint. This would help to reduce the computational time of my problem. Following constraint should be ...
Adri's user avatar
  • 11
1 vote
0 answers
87 views

Linearization of Conditional Constraints for MIP using Cplex

I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
B.Kim's user avatar
  • 11
0 votes
0 answers
76 views

Optimize revenue function with log part

I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function: $$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
MarcM's user avatar
  • 133
2 votes
1 answer
103 views

Representing a Multi-Level Categorical Variable using Big-M Method in Linear programming

I'm working with a statistical linear model where I have a variable, ( N ), representing the percentage of charging of a battery. Based on ( N ), I derive another variable, ...
MarcM's user avatar
  • 133
-1 votes
1 answer
71 views

How to linearize the multiplication of variables and transform this into an MILP?

Let $C=10$, $U=50$ $P_c,c=1,\cdots,C$ and $\alpha_{u,c},u=1,\cdots,U,c=1,\cdots,C$ are optimization variables $\alpha_{u,c}$ is binary $\sigma_{u,c}$, $d_{u,c}$ are known parameters $\min \sum_{c=1}^...
KGM's user avatar
  • 2,297
2 votes
1 answer
105 views

How to linearize the multiplication by a binary decision variable?

I am currently optimizing a hydrogen production chain. I am optimizing the production regime, and the size of the required wind, solar and the electrolyser. For every hour of the year, the production ...
KlaasR's user avatar
  • 23
4 votes
1 answer
186 views

Non-Linear objective function due to piecewise component

I have the following objective function: $\sum_{n}(1-prob_{n})(1+x_n)$ Where $x$ is my decision variable. $prob_{n}$ is a piecewise function that can look like: $prob_{n} = $ \begin{cases} 0.5, ...
akkha's user avatar
  • 67
4 votes
3 answers
347 views

Systematic references on linearizing conditional / logical expressions

On this site, one can usually finds questions like “How to transform my expression into linear form?” The expressions usually contain and, ...
Penghui Guo's user avatar

1
2 3 4 5 6