# Himmelblau 6 with the right hand sides of equalities 
# slightly modified to make the problem compatible, 
# but with Murtagh's and Saunders corrections of some of the equality constraints
# written in AMPL by Yu-Ju Kuo and Hans D. Mittelmann, 6/2001
param N;
param NH;
param NG;
param C{1..N};
param NK{1..7};
var  X{1..N}:=0.1;
var S1{i in 1..7}=if(i==1) then sum{j in 1..NK[i]}X[j] 
            else sum{j in NK[i-1]+1..NK[i]}X[j];
var S2{i in 1..7}=if(i==1) then sum{j in 1..NK[i]}X[j]*(C[j]+log(X[j]/S1[i])) 
            else sum{j in NK[i-1]+1..NK[i]}X[j]*(C[j]+log(X[j]/S1[i]));
minimize obj:sum{i in 1..7}S2[i];
s.t. HX1 :X[ 1]+X[ 5]+X[18]+X[32]+2.e0*X[33]+3.e0*X[34]+4.e0*X[35]-0.6529581e0=0;
s.t. HX2 : X[ 2]+X[ 6]+X[14]+X[15]+X[16]+X[19]+X[27]+X[28]+X[29]+X[43]+X[45]-  0.281941e0=0;
s.t. HX3 : X[ 3]+X[ 7]+X[20]-3.705233e0=0;
s.t. HX4 : X[ 4]+X[ 8]+X[13]+X[15]-X[16]+X[21]+X[26]+X[28]-X[29]+X[36]-X[38]+X[39]-X[41]-X[43]-X[45] - 47.00022e0=0;
s.t. HX5 : X[ 4]+X[ 9]+X[13]+X[14]+X[15]+X[16]+X[22]+X[26]+X[27]+X[28]+X[29]-47.02972e0=0;
s.t. HX6 : X[10]+X[23]-0.08005e0=0;
s.t. HX7 : X[11]+X[24]-0.08813e0=0;
s.t. HX8 : X[12]+X[25]-0.04829e0=0;
s.t. HX9 : X[17]-0.0155e0=0;
s.t. HX10: X[30]-0.0211275e0=0;
s.t. HX11: X[31]+X[32]+X[33]+X[34]+X[35]- 0.0022725e0=0;
s.t. HX12: X[ 8]-X[ 9]-X[10]+X[11]+X[12]-X[14]- 2.e0*X[16]-X[17]=0;
s.t. HX13: X[36]+X[37]+X[38]-4.e0*X[31]-3.e0*X[32]-2.e0*X[33] -X[34]=0;
s.t. HX14: -X[32]-2.e0*X[33]-3.e0*X[34]-4.e0*X[35]+ X[39]+X[40]+X[41]=0;
s.t. HX15: -4.e0*X[38]+X[42]+X[43]=0;
s.t. HX16:-4.e0*X[41]+X[44]+X[45]=0;
s.t. gi{i in 1..NG}: X[i]-0.000001>=0;

      
data;
param N:=45;
param NH:=16;
param NG:=45;
param NK:=1 4 2 17 3 35 4 38 5 41 6 43 7 45;
param C:=1 0 2 -7.69 3 -11.52 4 -36.6 5 -10.94 6 0 7 0 8 0 9 0 10 0 11 0 12 2.5966
         13 -39.39 14 -21.35 15 -32.84 16 6.26 17 0 18 10.45 19 0 20 -0.5 21 0 22 0 23 0
         24 2.2435 25 0 26 -39.39 27 -21.49 28 -32.84 29 6.12 30 0 31 0 
         32 -1.9028 33 -2.8889 34 -3.3622 35 -7.4854 36 -15.639 37 0
         38 21.81 39 -16.79 40 0 41 18.9779 42 0 43 11.959 44 0 45 12.899;