Declaring just one variable as integer

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1

Hi, I want to solve a problem with the Banch and Bound method with assistance of AMPL, however, when I want to declare just one variable as integer the program sends error.
I have been using this .mod file:

param n; #Nº de variables de decisión 
param m; #Nº de restricciones

param c{i in 1..n}; #Vector de coeficientes función objetivo
param a{j in 1..m, i in 1..n}; # Matriz de coeficientes de las restricciones
param b{j in 1..m};# vector de lados derechos

var x{i in 1..n} >=0 ; #Variabes de decisión

maximize valor: sum{i in 1..n} c[i] * x[i]; #Función objetivo

subject to Restricciones{j in 1..m}: 
   sum{i in 1..n} a[j,i] * x[i] <= b[j]; #Restricciones

If someone could teach me how to declare, for example just X[4] as an integer with value >=5 I would be extremely thankful.

That’s all. Good day.

2

See How do I relax the integrality of only some of a model’s integer variables? in our Frequently asked questions. Also, there is an example in a recent post about Relaxing integrality on specific index values of a variable.

For your example, you could define

var x {i in 1..n} integer >= 0;

and then use these statements to say that x[4] must be an integer that is >=5:

let {i in 1..n} x[i].relax := (if i = 4 then 0 else 1);
subject to LowerBound: x[4] >= 5;