# Dembo1b (the scaled version)
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001
param N:=12;
param NH:=0;
param NG:=15;
var X{1..N}:=4;
param ALF{1..11};
param AL2{1..4,1..9};
param AL3{1..3,1..5};
param GAMF;
param KF{1..11};
param K2{1..4,1..9};
param K3{1..3,1..5};
param GAM2{1..9};
param GAM3{1..5};
param DL2{1..N};
param DL3{1..N};
param UG{1..12};
var EXPO{i in 1..11}=exp(ALF[i]*log(abs(X[KF[i]])));
var EXPO2{i in 1..9,j in 1..4}=exp(AL2[j,i]*log(abs(X[K2[j,i]])));
var EXPO3{i in 1..5, j in 1..3}=exp(AL3[j,i]*log(abs(X[K3[j,i]])));
minimize obj: GAMF*EXPO[1]*EXPO[2]*EXPO[3]*EXPO[4]*EXPO[5]*EXPO[6]*
   EXPO[7]*EXPO[8]*EXPO[9]*EXPO[10]*EXPO[11];
s.t. gx1: (1.D0-5.36373D-2*X[1]-2.1863746e-2*X[2]-9.7733533e-2*X[3]
         -6.6940803e-3*X[4]*X[5])*10>=0;
s.t. gx2: 10*( 1+sum{i in 1..N}DL2[i]*X[i]+
        sum{i in 1..9}GAM2[i]*EXPO2[i,1]*EXPO2[i,2]*EXPO2[i,3]*EXPO2[i,4])>=0;
s.t. gx3: 10*(1+sum{i in 1..N}DL3[i]*X[i]+
        sum{i in 1..5}GAM3[i]*EXPO3[i,1]*EXPO3[i,2]*EXPO3[i,3])>=0;
s.t. gx4{i in 4..NG}: 100*(X[i-3]-UG[i-3])>=0;




data;
param KF:=
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
11 11;
param GAMF:=100000;
param ALF:=
1  -0.001331720e0
2 -0.002270927e0
3 -0.00248546e0
4  -4.67e0
5 -4.671973e0
6 -0.00814e0
7 -0.008092e0
8   -.005e0
9 -.000909e0
10 -0.00088e0
11 -0.00119e0;
param GAM2:= 
1 -1.e-9
2 -1.e-9
3 -1.e-3
4 -1.e-3
5 -1.0898645e-1
6 -1.6108052e-5
7 -1.0e-23
8 -1.9304541e-8
9   -1.e-4;
param GAM3:=
1 -1.0898645e-1
2 -1.6108052e-5
3 -1.e-23
4 -1.9304541e-8
5 -1.1184059e-4;
param AL2 (tr):=
:   1   2    3       4 :=
1 1.e0 1.e0 0.0e0 0.0e0
2 1.e0 -1.e0 0.e0 0.e0  
3 1.e0  -1.e0  0.e0  0.e0     
4 1.e0  1.e0  0.e0  0.e0  
5  1.e0  1.e0  0.e0  0.e0  
6 1.e0  1.e0  -1.e0  0.e0  
7  1.e0  1.e0  1.e0  0.e0  
8 1.e0  -1.e0  1.e0  -2.e0  
9 1.e0  -1.e0  0.e0  0.e0;
param K2 (tr):=
:   1 2  3 4 :=
1   4  12  0  0   
2   5  12  0  0   
3   6  12  0  0  
4   7  12  0  0     
5   4  5  0  0  
6   2  5  12  0   
7   2  4  5  0  
8   2  4  4  12  
9   10  12  0  0;
param   AL3 (tr):=
: 1      2   3:=
1 1.e0  1.e0  0.e0  
2 1.e0  1.e0  0.e0   
3 1.e0  1      1
4 1.e0  -1.e0  1.e0  
5 1.e0  1.e0  0.e0;
param K3 (tr):=
: 1 2 3:=
1 4  5  0   
2 2  5  0  
3 2  4  5  
4 2  4  5  
5 1  9  0;
param UG:=
1 .1
2 .1
3 .1
4 .01
5 1
6 .1
7 .1
8 .1
9 .1
10 .1
11 .1
12 .1;
param DL2:=
1 -1.e-6  
2 -1.e-5  
3 -1.e-6  
4 0.e0
5 0
6 0
7 0
8 0
9 0
10 0
11 0
12 0;
param DL3:=
1 -1.e-6  
2 -1.e-5  
3 -1.e-6  
4 -1.e-9  
5 -1.e-9  
6 -1.e-3  
7 0.e0  
8 -1.e-3  
9 -1.e-5  
10 0.e0  
11 -1.e-4  
12 0.e0;