# Linked Questions

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I have a continuous variable $c$ which has value in between $[-R, +R]$. I want to create a boolean variable $x$ and, $x = 1$ when $c = 1.0$ otherwise $x = 0$ In more general form: $x = 1$ when $c \... 2answers 834 views ### In an integer program, how can I “activate” a constraint only if a decision variable has a certain value? Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where$a_i$and$b$are constants and$x_i$are decision variables. Suppose also that we want the constraint to hold if$y=1$(... 1answer 2k views ### How to formulate (linearize) a maximum function in a constraint? How to formulate (linearize) a maximum function in a constraint? Suppose$C = \max \{c_1, c_2\}$, where both$c_1$and$c_2$are variables. If the objective function is minimizing$C$, then it can be ... 1answer 1k views ### If-then constraints in MIP programming For continuous variables$x$and$y$, the constraints are: ... 3answers 333 views ### Find the farthest point in hypercube to an exterior point Let$\mathcal{U} = \{ [x_1, ..., x_n] \in \mathbb{R}^n : 0 \leq x_i \leq 1\}$be the unit hypercube and$C \in \mathbb{R}^n\setminus\mathcal{U}$fixed. Let us consider the following problem $$\max_{X ... 2answers 178 views ### Conditional Constraint in MIP I need to formulate a conditional constraint for a binary variable z defined as: z_{i,j,k}, \ \ i=1:10 \ , \ j=1:5 \ , \ k=1:3 If any z_{i,j,3} = 1 then z_{i,j,1} + z_{i,j,2} = 0 \ \ \... 2answers 291 views ### How to model If A \le B then Y = 1, otherwise Y = 0 Somehow I don't get it right. I would like to model the following conditional: If A\le B then Y=1 otherwise Y=0 where A, B are reals and Y is binary. I can model as follows: Y \cdot A \le B... 1answer 143 views ### Conditional Controls in MIP Models Innocently cross-posted at Mathematics SE I am developing a model that operates in the realm of mixed integer programming, although I am fairly unfamiliar with this area of mathematics at the moment. ... 2answers 294 views ### Mocking up conditional statements in LP I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically: 1. Is it ... 1answer 96 views ### Binary variable to count appearances Let x \in \mathbb{R}^n be an optimization variable. Now, at a constraint, I would like to count how many times a value, say 2, appears in x decision. I think we can have a binary variable y_i... 1answer 69 views ### How to model A_i=B_i for only one i I would like to model the following: Only one of the following equalities can hold.$$(A_1 = B_1)\quad\text{OR}\quad(A_2 = B_2)\quad\text{OR}\quad\dots\quad\text{OR}\quad(A_k = B_k)$$I can ... 1answer 127 views ### Linearizing constraint with continuous and boolean variables I have two continuous variables A, B and two binary variables x, y. Condition: if A = B \wedge x = 1 \wedge y=1 then z = 1 else z = 0 from In an integer program, how I can force a ... 1answer 87 views ### Same values constraint and grouping of variables In a linear program, I would like some variables to: 1. Take the same values 2. Group some variables i.e. some variables should take same values or lie within certain percentage. 3. All different ... 1answer 118 views ### How to optimize with “if” constraints The minimizing problem is the following :$$ \underset{w}{\operatorname{argmin}} \sum_{i=1}^{n}\left[w_{i}\times (\frac{Vw}{\sigma})_{i} - b_{i}\right]^{2}$$with$V$a$n\times n$matrix (covariance ... 0answers 91 views ### Conditional constraint formulation [duplicate] How can I create constraints to make sure$x=1$if$k\geq 0$and$x=0$if$k<0$, where$x\in \{0,1\}$and$k\in \mathbb{R}\$? Here is my attempt: \begin{equation}\label{cons:1} \begin{aligned} ...

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