# Questions tagged [reformulation-linearization]

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### Linearize piecewise function without big-M constraints

I have been attempting to solve a maximization problem where there is a piecewise function in the objective. Something like: $\sum_{n}(1-prob_{n})(1+x_n)$ Where $prob_{n} =$ \begin{cases} 0.25,...
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### Change the objective function formula change the complexity of a linear program?

I have a linear program, where I can use it with the same constraint to minimize objective 1 or minimize objective 2. I noted that when I use the formula of objective 2 the problem can be solved with ...
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### DCP formulation of sum of nonconvex and convex functions

I am trying to find a DCP formulation for the following convex objective function (using CVXPY): Let $x$ be the $N$-dimensional vector variable on which we optimize on, $c$ be a known scalar value ...
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### Linearize a product of binary variables

I have a function to minimize which has the following term $$\sum_{i\in I}\sum_{j\in J}\sum_{k\in K}x_{ijk}N_{ij}a_{ijk},$$ where the variables are $x_{ijk}\in\{0,1\}$, $a_{ijk}$ are given as input ...
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### How to treat a system of bilinear constraints

A model contains constraints of the following form $R(k) \leq X(k) G(k)$ where $X(k)$ binary and $G(k)$, $R(k)$ non-negative variables. The index $k$ runs from $1$ to $50$. I linearise the equations ...
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### Piecewise linear and global optimization

I am new to OR, and apologies if my mathematical notation is not clear. I have tried my best to keep it concise and given an explanation with numerical data. I would like to understand: Can this ...
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### How to deal with an optimization problem that have a sum of nonlinear functions of Z as a constraint when Z is the quantity to be minimized?

I have to minimize a quantity $Z$ subject to the following constraints: $$w_1 + w_2 + w_3 = 1 \tag{1}$$ $$\frac{f_1(w_1 Z) + f_2(w_2 Z) + f_3(w_3 Z)}{Z} \ge k \tag{2}$$ where $k$ is a known ...
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### Maximizing a Ratio/Percent

I'm using cvxpy to model a problem. Inside a very large and complex LP, I create two continuous, affine (unconstrained) expressions: $x$ and $y$. Due to how they ...
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### Switching of decision variables to be equal to a certain decision variable according to a binary (indicator) variable

I would like to seek some advice on modeling the following: I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third ...
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### Formulating indicator constraint set

I am having difficulty formulating the indicator constraints for the following: Consider a set of $A_{n}$ decision variables such that $A_{1},A_{2},⋯,A_{n}<A$. While all of them are integers that ...
• 707
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### Reformulating to locate the second largest decision variable of a set of decision variables

Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the ...
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### Linearize sum of continuous and boolean variable

For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
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