# Questions tagged [linearization]

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

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### Linearized formulas and constraints

I am researching how to linearize the maximum and minimum functions in optimization problems and have encountered some confusion. I am linearizing an equation, and ...
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### partial feedback linearization with observation

I am considering a partial feedback linearization system with relative degree 2. I have to stabilize a state $x_1$, during estimating $x_2$. Can I describe it below? and recommendation for book and ...
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### Which nonlinear PDEs can be converted into linear PDEs?

In Section 4.4 of Partial Differential Equations by Evans, the author describes several techniques for converting certain nonlinear equations into linear equations. First, the author introduces the ...
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### What is the proper way of interpreting "linearizing a differential equation"? [closed]

Suppose we have the following differential equation: $$\ddot{\theta} + \cos{\theta} = 0 \quad,$$ where $\theta$ is an unknown function of a real variable. It isn't uncommon to say we will "...
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### 0-1 Linear programming and non-optimal multidimensional knapsack

I would like to create a set of constraints forcing a set of knapsacks to be filled. The knapsacks should be filled, so that no further element of a set of elements fits into it. It is not a classical ...
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### Tractable formulation of a mixed integer program

Given constant matrices $A_1\in\mathbb{R}^{1\times l}$ and $A_2\in\mathbb{R}^{1\times l}$, and constants $b_i$, $i=1,\dots,n$. Consider the following mixed integer program (MIP) with decision ...
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### SQP and first order Taylor approximation

I am trying to use the SQP solver with a nonlinear constraint. The solver requires a linear constraint so I am trying to approximate the constraint with the first-order Taylor approximation. Is this ...
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### How to linearize time-variant ordinary differential equation (ODE), in particular, if there is a convolution term?

Letting $(\ * \ )$ denote convolution, I have an ODE of the form \begin{align} \dot{r} &= -7.4r -1.6f - 8.8 (f(t)*e^{-t}) - 10.4(f(t)*(te^{-t})) \\ \dot{f} &= 0.25r \end{align} with initial ...
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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 ...
1 vote
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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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I am given the equations of motion: $$\dot{r} = f(r)p_r,$$ $$\dot{p_r} = -\frac{V'(r)}{2f(r)}-\frac{f'(r){p_r}^2}{2}+\frac{V(r)-E^2}{2f^2(r)}f'(r)$$ Along with the conditions that E^2-V(r_0)=V'(r_0)=...