function myerf;

param l {1..4};
param u {1..4};

var x {j in 1..4} >= l[j], <= u[j];

param a := 0.0001;
param b := 1;
param d := 1;
param n := 24;

minimize obj: 
  ( a*n - (b*(exp(x[1])-1) - x[3])*x[4]/(exp(x[1]) - 1 + x[4]) )/x[1]
  ;

subject to constr1: 
    x[3] - 2*myerf(-x[2]) = 0;
subject to constr2: 
    x[4] = myerf(-x[2] + d*sqrt(n)) + myerf(-x[2] - d*sqrt(n));

data;

param l := 
  1  0.0001
  2  0
  3  0
  4  0
  ;

param u := 
  1  100
  2  100
  3    2
  4    2
  ;

let x[1] := 1;
let x[2] := 1;
let x[3] := 1;
let x[4] := 1;

#printf "optimal solution as starting point \n";
#let x[1] := 0.06785874;
#let x[2] := 3.6461717;
#let x[3] := 0.00026617;
#let x[4] := 0.8948622;

display obj;

option pl_linearize 0;

solve;

display x;

display obj;

display obj + 0.920425026;