# -----------------------------------------------------------------
# Reference:
# @book{Numerica,
# author    = {P. {Van Hentenryck} and L. Michel and Y. Deville},
# title     = {{N}umerica: a {M}odeling {L}anguage for {G}lobal {O}ptimization},
# publisher = {MIT Press},
# year      = {1997}
# }
# 
# Solution 1 [5.54e-08]
# X1 = 0.899999952617 + [-6.856e-12 .. +6.857e-12]
# X2 = 0.449987471982 + [-5.649e-09 .. +5.649e-09]
# X3 = 1.00000648247  + [-2.081e-08 .. +2.081e-08]
# X4 = 2.00006854163  + [-1.712e-08 .. +1.712e-08]
# X5 = 7.99997144049  + [-2.769e-08 .. +2.769e-08]
# X6 = 7.99969268422  + [-3.162e-09 .. +3.162e-09]
# X7 = 5.00003127593  + [-1.317e-08 .. +1.317e-08]
# X8 = 0.999987723457 + [-1.395e-09 .. +1.395e-09]
# X9 = 2.00005248349  + [-1.339e-09 .. +1.339e-09]
# 
# Y0 = 0.595011296539 + [-1.157e-09 .. +1.157e-09]
# Y1 = 0.595015153679 + [-4.772e-10 .. +4.772e-10]
# Y2 = 1.19006337612  + [-3.959e-11 .. +3.959e-11]
# 
# 
# 
# Solution plus precise:
# 
# Solution 1 [9.46e-13]
# X1 = 0.899999952617 + [-5.552e-16..+5.552e-16]
# X2 = 0.449987471982 + [-4.913e-14..+4.913e-14]
# X3 = 1.00000648247 + [-1.111e-13..+1.113e-13]
# X4 = 2.00006854163 + [-1.315e-13..+1.315e-13]
# X5 = 7.99997144051 + [-2.177e-13..+2.185e-13]
# X6 = 7.99969268422 + [-4.726e-13..+4.726e-13]
# X7 = 5.00003127594 + [-1.857e-13..+1.857e-13]
# X8 = 0.999987723457 + [-1.91e-14..+1.91e-14]
# X9 = 2.00005248349 + [-1.115e-13..+1.12e-13]
# Y0 = 0.595011296539 + [-4.042e-14..+4.053e-14]
# Y1 = 0.595015153679 + [-3.009e-14..+3.02e-14]
# Y2 = 1.19006337612 + [-8.816e-14..+8.816e-14]
# -----------------------------------------------------------------





# Domains
var X1 >= 0, <= 10;
var X2 >= 0, <= 10;
var X3 >= 0, <= 10;
var X4 >= 0, <= 10;
var X5 >= 0, <= 10;
var X6 >= 0, <= 10;
var X7 >= 0, <= 10;
var X8 >= 0, <= 10;
var X9 >= 0, <= 10;
var Y0 >= -1000, <= 1000;
var Y1 >= -1000, <= 1000;
var Y2 >= -1000, <= 1000;


# Constants
param G_1_1 := 0.485;
param G_2_1 := 0.369;
param G_3_1 := 5.2095;
param G_4_1 := 23.3037;
param G_5_1 := 28.5132;
param G_1_2 := 0.752;
param G_2_2 := 1.254;
param G_3_2 := 10.0677;
param G_4_2 := 101.779;
param G_5_2 := 111.8467;
param G_1_3 := 0.869;
param G_2_3 := 0.703;
param G_3_3 := 22.9274;
param G_4_3 := 111.461;
param G_5_3 := 134.3884;
param G_1_4 := 0.982;
param G_2_4 := 1.455;
param G_3_4 := 20.2153;
param G_4_4 := 191.267;
param G_5_4 := 211.4823;


subject to
cons1 : X1*X3 = X2*X4;
cons2 : X1*X2 = 1-Y0;
cons3 : Y1 = Y0*X3;
cons4 : Y2 = Y0*X4;

cons5 : Y1*(exp(X5*(G_1_1 - G_3_1*X7*0.001 - G_5_1*X8*0.001)) - 1) = G_5_1 - G_4_1*X2;
cons6 : Y1*(exp(X5*(G_1_2 - G_3_2*X7*0.001 - G_5_2*X8*0.001)) - 1) = G_5_2 - G_4_2*X2;
cons7 : Y1*(exp(X5*(G_1_3 - G_3_3*X7*0.001 - G_5_3*X8*0.001)) - 1) = G_5_3 - G_4_3*X2;
cons8 : Y1*(exp(X5*(G_1_4 - G_3_4*X7*0.001 - G_5_4*X8*0.001)) - 1) = G_5_4 - G_4_4*X2;

cons9 : Y2*(exp(X6*(G_1_1 - G_2_1 - G_3_1*X7*0.001 + G_4_1*X9*0.001)) - 1) = G_5_1*X1 - G_4_1;
cons10 : Y2*(exp(X6*(G_1_2 - G_2_2 - G_3_2*X7*0.001 + G_4_2*X9*0.001)) - 1) = G_5_2*X1 - G_4_2;
cons11 : Y2*(exp(X6*(G_1_3 - G_2_3 - G_3_3*X7*0.001 + G_4_3*X9*0.001)) - 1) = G_5_3*X1 - G_4_3;
cons12 : Y2*(exp(X6*(G_1_4 - G_2_4 - G_3_4*X7*0.001 + G_4_4*X9*0.001)) - 1) = G_5_4*X1 - G_4_4;

solve;
display X1, X2, X3, X4, X5, X6, X7, X8, X9, Y0, Y1, Y2;