# Himmelblau13 (Box)
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001
param N;
param NH;
param NG;
param XK{1..5};
param XKH{1..30};
param XKG{1..16};
var X{1..N};
var H{i in 1..6}= XKH[(i-1)*5+1]+sum{k in 2..5}XKH[(i-1)*5+k]*X[k];
minimize obj:-(50.e0*X[9]+9.583e0*X[10]+20.e0*X[11]+15.e0*X[12]-852.96e3-38.1e3*(X[2]+0.01e0*X[3])
          +XK[1]+XK[2]*X[2]+XK[3]*X[3]+XK[4]*X[4]+XK[5]*X[5])*X[1]-15.e0*X[6];
s.t. hx1: X[6]-H[1]*X[1]=0;
s.t. hx2{i in 2..5}:X[i+7]-H[i]=0;
s.t. hx6: X[8]-(H[6]*X[1]+X[6]+X[7])=0;
s.t. hx7: X[7]-(X[9]+X[10]+X[11])*X[1]=0;
s.t. gx{i in 1..8}: X[i]-XKG[i]>=0;
s.t. gx2{i in 9..NG}:XKG[i]-X[i-8]>=0;


data;
param N:=12;
param NH:=7;
param NG:=16;
var X:=
1 2.52
2 2.00
3 37.5
4 9.25
5 6.80
6 32745.827
7 96991.969
8 130368.43
9 21430.114
10 4016.7717
11 13041.991
12 7619.5782;
param XK:= 
1 925548.252
2 -61968.8432
3 23.3088196
4 -27097.648
5  -50843.766;
param XKH:=
1 -145421.402
2 2931.1506
3 -40.427932
4 5106.192
5 15711.360
6 -161622.577
7 4176.15328
8 2.8260078
9 9200.476
10 13160.295
11 -21686.9194
12 123.56928
13 -21.1188894
14 706.834000
15 2898.5730
16 28298.388
17  60.8109600
18 31.242116
19 329.5740000
20 -2882.082
21 74095.3845
22 -306.262544
23 16.2436490
24 -3094.252
25 -5566.2628
26 -26237.000
27 99.0
28 -0.42
29 1300
30 2100;
param XKG:=
1 0.0
2 1.2
3 20.0
4 9.0
5 6.5
6 0.0
7 0.0
8 0.0
9 5.0
10 2.4
11 60
12 9.3
13 7.0
14 294000
15 294000
16 277200;