# Euclidean single facility location problem

# Objective Function:  convex
# Constraint Functions: none

param d := 2;		# dimension
param m := 1000;		# number of facilities

param a {1..m, 1..d};   # coordinates of existing facility
param w {1..m};		# weight associated with each existing facility

var x {1..d};
var t {1..m};

minimize sumEucl: sum {i in 1..m} w[i]*t[i];

subject to t_def {i in 1..m}: 
    sqrt( sum {j in 1..d} (x[j] - a[i,j])^2 ) <= t[i];

let {i in 1..m, j in 1..d} a[i,j] := Uniform01();
let {i in 1..m} w[i] := Uniform01();

let {j in 1..d} x[j] := 0.5;

solve;

display x;