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# 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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### How to reformulate (linearize/convexify) a budgeted assignment problem?

I have a scheduling problem at hand. In my system, there is a service station with $M$ service outlets, therefore, the service station can serve $M$ users at a time. But, there are $N$ users $N>M$ ...
235 views

### How to deal this L0 norm of a vector of L2 or L1 norms in objective?

I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=[{\bf a}_1\hspace{1mm} {\bf a}_2 \hspace{1mm} {\bf a}_3 \hspace{1mm} {\bf a}_4 \hspace{1mm} {\bf a}_5];$ Here, ${\bf a}_1$...
104 views

### How to linearize or fix this disciplined convex programming error?

How can I linearize this constraint $$d_{u,c}\sigma \le \|{\bf f}_{u,c}\|^2\le Td_{u,c}$$ $\sigma$ is a very small number based on scale of $f$ $T>0$, ${\bf f}_{u,c}$ is optimization variable, a ...
33 views

### Choosing upper and lower bound using big-M [duplicate]

This question is related to my previous question posted here: Piecewise constraint using big-M notation and this question posted on the math stackexchange: https://math.stackexchange.com/questions/...
1 vote
68 views

### MILP: Substituting products with additive logarithms

I would like to linearize a product, for example $a*b$. if I solve my solution in log space, I can formulate it as $a+b$ and when my final output is returned, remember to convert back to original ...
165 views

### How to solve a "nearly" linear program

Given a positive integer $n$, a constant $k=2/3$, and $7$ variables $x_1, x_2, x_3, x_{12}, x_{13}, x_{23}, x_{123}$ (non-negative reals or integers) I would like to find: $$\min \binom{x_1}2$$ ...
9k views

### How to linearize the product of a binary and a non-negative continuous variable?

Suppose we have a binary variable $x$ and a non-negative continuous variable $y$. How can we linearize the product $x y$?
197 views

### MIP constraint with sum of decision variables having certain value : $\sum_{i=1}^nx_i = 2 \implies \delta = 1$

I want to formulate a MIP constraint such that : $$\sum_{i=1}^nx_i = 2 \implies \delta = 1$$ $x_i, \delta \in \{0, 1\}$. My problem is that delta should be one when this sum is exactly 2 and not ...
115 views

### Multiple absolute values with multiple variables in an LP

Assume that we have a LP with the constraint $$\sum_{j} \left(c_j x_j + |c_j x_j - \alpha_j + \beta_j|\right) \leq y$$ and $$\alpha_j + \beta_j \leq \lambda_j$$ for all $j$, where the (positive) ...
63 views

### Outer approximation approach for MINLP

Does anybody know why in the outer approximation approach for MINLP it is not necessarily/needed to solve MILP to optimality? What is the rationale or explanation behind it?
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### Linearize a higher order polynomial objective function?

My question up front with context below: Is there a generalized linearization possible for a higher order polynomial (max degree 6 in my case) involving a mix of binary and real variables? If not, ...