# Questions tagged [linearization]

On the many different ways to turn non-linear systems of equations into linear ones.

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### Linear optimization with max function in constraint

I have a linear optimization: $$\min_{x_i} -\sum_i x_i$$ $$\mathrm{s.t.} Ax \le b$$ Where $x$ is a variable vector. I would like to introduce into the linear problem an additional constraint that ...
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### Linearising a polynomial using logs

I have been a bit rusty with my natural logs. I want to linearize this polynomial using logs. Does this look correct? y = (v-x)/x^2 ...
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### Eigenvalues of Jacobian around non-stationary points

This is a two-part question Part 1 We have often done stability analysis by calculating the eigenvalues of the Jacobian of a nonlinear function around a stationary solution. I accidentally repeated ...
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### Linearization of constraint in linear programming

I have the following decision variables: $x$, which is binary, and $a, b, c > 0$, which are continuous. I would like to express in linear form for a linear programming model the following ...
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### In linear-fractional programming why can't we require denominator to be equal to one without introducing a new variable?

Usually, linear-fractional programming problems are solved by transforming them into equivalent linear programming problems. That is done using Charnes-Cooper method which involves introducing a new ...
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### How to linearize a weighted average using Pyomo?

I'm learning about linear optimization problems using Pyomo. At this time I'm looking to practice and ended up getting stuck in a constraint that contains the weighted average formula. Using this ...
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### How to model this constraint linearly in binary integer linear programming?

I have a directed acyclic graph, and two binary decision variables: $a_{ij}$, which is equal to one when the corresponding edge between the nodes $i$ and $j$ of the graph is selected, and zero ...
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### Two approaches to change the absolute value in Linear Programming

Usually a MP with absolute value $|x|$ can be linearlize by using the transformation of $$|x|=x^++x^- \ \ and \ \ x=x^+-x^-. (A)$$ But I find someone also use $$y\geq x \ \ and \ \ y\geq -x. (B)$$...
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### Linearize tricky constraint to MILP, LP

It's hard to describe this constraints. Please check this: It is a selection problem. Item Name Brand Value Price item 1 A 0.1 0.2 item 2 B 0.2 0.3 item 3 A 0.1 0.3 We want to select several ...
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### Linearizing product of binary variables

How would I linearize the following expression $$z = (1-x)y$$ where $x,y \in \{0,1\}$? Ideally, I would want to formulate this as a system of linear inequalities.
I have an optimization problem where I have two sets containing $n$ items, which I must place inside $m$ arrays with the same capacity $c$. The cost of each array is equal to the cost of the most ...
In Euclidean space, if I have a smooth dynamical system $\dot{x}=F(x)$, it's linearization about a solution $x(t)$ is $\dot{v}(t) = DF(x(t))v(t)$, where $DF(x)$ is the Jacobian matrix of $F$ at $x$. I ...