# Questions tagged [linearization]

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

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### Linearize max function in a constraint [duplicate]

I have a constraint as follows: $\sum_i {r_i} \geq \max \{g_j, B_j\}$ where, $r_i$, $g_j$ are variables and $B_j$ is a parameter. How do I linearize the constraint (I suppose using big-M method)?...
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### Linearize a product of an integer variable (not just binary) and a continuous variable?

I have a constraint in my formulation that contains multiplication of an integer variable $y$ and a continuous variable $x$, which is $xy=q$ where $y$ is the number of units in which $q$ gets equally ...
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### Problem with binary decision variable constraints in VRP

I would like to create non-linear violation costs in my VRP. I already created my whole VRP with time windows in which I have these decision variable: ...
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### Inequality Constraint Linearization of a product of an integer and a binary variable

I have thought I had found the answer here: How to linearize the multiplication of an integer and a binary integer variable? But the answers to that questions didn't help me find a solution for my ...
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### How to linearize a weighted maximum coverage problem?

Is it possible that the binary variables below be modeled as continuous variables? \begin{alignat}2\max&\quad\sum _{{e\in E}}w(e_{j})\cdot y_{j}\\\text{s.t.}&\quad\sum {x_{i}}\leq k,\quad&...
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### Minimizing $x_1/x_2$ over a simplex in the positive orthant

I need to solve the following problem \begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix. The best thing I can think ...
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### Mocking up conditional statements in LP

I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically: 1. Is it ...
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### Linearizing objective function with variables inside an indicator function

I am working on a problem in which I am trying to maximize the average of a variable only for the data that meet a certain condition with a constraint on the number of data that meet this condition. I ...
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### Transforming a Quadratic constraint to SOCP

I have a problem similar to Markowitz portfolio optimization that I would like to transform into second-order cone programming. I have a linear objective function with a quadratic constraint (assuming ...
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### if-else condition for the objective variable using big M notation

Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$. Now, how can I impose the following? if $\beta_{i,j}>0$ then $\beta_{j,i}=0$ Big M notation can be ...
I have a minimization problem minimizing $d_k \geq 0$ and some other variables with all strictly positive coefficients. I leave my objective function below to better convey my goal. $$\min_{\mathbf{d}... 1answer 123 views ### Linearizing the square root of binary summations My question is similar to this one and almost identical with this. I am so confused due to indexing and could not make sure if I could apply the solution in here to this indexed version as shown below.... 1answer 58 views ### Linearizing the square root of two binary summations My question is similar to this one though a bit more complicated. Though my question also includes indices, I am removing them to ease readability. Let binary variables x,y\in\{0,1\}, non-negative ... 2answers 998 views ### Linear programming: objective function with “buckets” I had a linear programming problem with the following objective function$$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$Where q, p, C, c are known. This problem was ... 1answer 42 views ### defining Mixed integer linear inequalities for a set of variables The problem is described as follows: considering n variables which are continuous and bounded such that$$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.How can i define a set of mixed integer ... 2answers 263 views ### How to model If A \le B then Y = 1, otherwise Y = 0 Somehow I don't get it right. I would like to model the following conditional: If A\le B then Y=1 otherwise Y=0 where A, B are reals and Y is binary. I can model as follows: Y \cdot A \le B... 2answers 197 views ### Trade off between number of constraints and bounds of a variable I am not familiar with the inner working of the solvers. I mostly use the python pulp or IBM CPLEX solver. For fast execution ... 1answer 109 views ### Linearizing constraint with continuous and boolean variables I have two continuous variables A, B and two binary variables x, y. Condition: if A = B \wedge x = 1 \wedge y=1 then z = 1 else z = 0 from In an integer program, how I can force a ... 1answer 61 views ### How to formulate case distinctions in AMPLs objective function? This is my first real optimisation problem I formulated and now trying to solve by using AMPL. The following objective function is from a linear 0-1 LP means all variables x_i^b\in\{0,1\}, with i\... 0answers 36 views ### Extract binary value from continuous variable [duplicate] I have a continuous variable c which has value in between [-R, +R]. I want to create a boolean variable x and, x = 1 when c = 1.0 otherwise x = 0 In more general form: x = 1 when c \... 0answers 64 views ### Converting Nonlinear Program into an LP I have a problem with a nonlinear objective function which is \begin{align}\min&\quad Z_j\cdot(N_j)^{0.5}\end{align} where j is the index. I want to know how can I turn it into a linear ... 1answer 147 views ### How to propagate time using linear inequalities? I have an adjacency matrix G_{i,j} that tells the distance between i to j (between 0 to 1) if there is no edge between i to j I am putting a large integer 100. This is my previous ... 1answer 74 views ### Linearizing objective function with absolute differences I want to turn this objective function\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T| where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector ...
I am trying to model a grouping algorithm as k-means clustering problem, by referring to the general definition as mentioned in Wikipedia. In my system, I have $N$ nodes that I want to group in $m$ ...