Questions tagged [linearization]
For questions related to techniques for converting nonlinear expressions in optimization models into equivalent (or approximately equivalent) linear ones.
259
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How to linearize a chain of if-then constraints?
How can I express the process of converting a series of if-then constraints into a linear form?
Let's assume that we have integer variable $x_i$, non-negative variables $y_i^d$, and binary variables $\...
- 177
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How to linearize such a constraint?
My original content was like this:
Assuming that server $k$ can only allocate corresponding computing functions to MU $i$ after receiving their tasks. Let
$$ y_{i,k,t} = \begin{cases} 1 & \text{if ...
- 11
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$\min\{f(x_1),\dots,f(x_n)\}$ with other constraints
I have an optimization problem which goes:
\begin{align*}
\text{Minimize:}
\\
& \sqrt{x} + \sqrt{y} \tag{NL-objective}
\\
\text{Subject to:}
\\
&3x + 2y \geq 2 &...
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396
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How to model a binary variable?
I am trying to find a constraint for the following relationship, but am failing a bit at it right now. I want to find a linear constraint that does the following. The binary variable $switch_{ot}$ is ...
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Rewriting if-then constraints of binary summations
Suppose both $x_{i,j}^{ab}$ and $y_{i,j}^a$ are binaries. Then how can I rewrite the following if-then in linear form?
$\sum_b x_{i,j}^{ab} \ge 1 \implies \sum_{i,j} y_{i,j}^a = 0$
I was thinking of ...
- 177
3
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2
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716
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Writing a constraint of an integer programming in a linear form
I modeled an optimization problem in an integer programming format. The main constraint I came up with is now nonconvex. I would like to see if there is another equivalent formulation in which the ...
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380
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How to model $C_1=C_2$ implies $b_1 = b_2$
Suppose $C_1 \ge 0$, $C_2 \ge 0$ are continuous variables and $b_1$, $b_2$ are binary variables.
How could I model the following?
$C_1 = C_2 \implies b_1 = b_2$, the opposite does not hold.
- 2,252
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Resource selection problem with non-linear objective function
I have an optimisation problem to solve but I can't model it correctly. Any insight is welcome :)
It has been a few years since my optimisation classes in university, and while I have forgotten a lot ...
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3
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3
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286
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Quantifying a measure of standard deviation in MILP
I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
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Linearization the product of three variables (two binary & one continuous)
Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$.
I am trying to model the following conditional equations as constraints:
\begin{cases}
...
- 113
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How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$
Some modeling languages and solvers support indicator constraints of the form $$y=\hat{y} \implies \sum_j a_j x_j \le b,$$ where $y$ is a binary decision variable and $\hat{y}\in\{0,1\}$ is a constant....
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Equivalence between constraints in ILP
Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that
$$ z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$
If I wanted to express the equivalence between ...
- 133
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Linearize conditional constraint
Consider a variable c from the domain {-1,0,1}. I have the following constraint:
IF $c = 1 \Rightarrow x = 1 $ ELSE $x = 0$
How do I linearize this constraint?
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The linearization of the logical constraints
I know the logical constraints can be linearized by either the logical representation of whose relation, (for pure binary variables e.g. CNF/DNF) or for general form by using Big-M formulation. As I ...
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The linearization of the (Iff-and-only-Iff) expression
I am trying to linearize the following expression without using the Big-M formulation, but I cannot convert it. I am willing to know if there exists an efficient way to do that?
$$ Iff \quad (w=1) \...
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