# 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 function

I have a facility location problem with a non-linear objective; There are fixed costs $S_j$ to opening facility $j$ $Y_j$ is a binary, $1$ if facility $j$ is opened, $0$ otherwise $D_j$ is the number ...
1 vote
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### Converting quadratic constrains to linear constraint [closed]

I try to convert a quadratic constraint to a linear one: $$w_j = \sum w_\text{j,i} \\ w_\text{j,i} = \frac{w_j}{D} \times u \\ w_j,D,u \in \mathbb{N} \\$$ The values for $w_j$ and $D$ are constant ...
547 views

### How to solve Rogo Puzzle with an extra constraint?

Given a n×m grid with numbered cells and forbidden cells, the objective of the Rogo puzzle is to find a loop of fixed length through the grid such that the sum of the numbers in the cells on the loop ...
1 vote
84 views

I have been dealing with a problem for sometime and although tried different things and asked some questions before, I think the problem might be somewhere that we didn't look before. Variables $0\le ... 2 votes 1 answer 72 views ### Linearizing$y=\sum_{i=1}^n(z+c)\left(\frac{r_i^2}{1-r_i}\right)\phi_i$Variables$0\le x< 1$,$y,z\ge 0$. We have a constraint $$y=(z+c)\frac{x^2}{1-x},$$ where constant$c>0$. We partitioned$x$into$n$intervals of equal length and defined a new variable$\phi_i=... 1k views

### How to use condition in cplex?

I want to use conditions to my variable. dvar boolean x[I][J][K][L] dvar in h[i] my code is ...
116 views

### Linearizing this absolute difference objective function $\min\sum_{i=1}^{I}\sum_{j=1}^{i}|x_i-x_j|$

For $x_i>0, i=1,\ldots,I$, I tried to linearize this objective function $$\min\sum_{i=1}^{I}\sum_{j=1}^{i}|x_i-x_j|$$ as $$\min\sum_{i=1}^{I}\sum_{j=1}^{i}y_{ij}$$ subject to \begin{align} & y_{... 484 views

### How to measure the tightness of MILP models?

Suppose we have a MILP model. How can we say this model is tight or not? How to make it more tight? Any advice or example?
807 views

### Knapsack - How to optimize bonuses for each pair of items

I am trying to solve a variation of the knapsack problem where every pair of items in my knapsack has a bonus or penalty associated with it. My knapsack can hold a dozen items There are thousands of ...