https://stackoverflow.com/questions/22475330
italiano
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RussianI don't have access to Mathematica, I put your equations into AMPL which is free for students. Here is what I did:
var w := 14 >= 0;
var x := 15 >= 0;
var y := 10 >= 0;
var z := 100 >= 0;
eq1: 7*w = (7*w+5*x+2*y+z) * ( 0.76 + 0.12*log(w) -0.08*log(x) -0.03*log(y) -0.07*log(7*w+5*x + 2*y + z));
eq2: 5*x = (7*w+5*x+2*y+z) * ( 0.84 - 0.08*log(w) +0.11*log(x) -0.02*log(y) -0.08*log(7*w+5*x + 2*y + z));
eq3: 2*y = (7*w+5*x+2*y+z) * (-0.45 - 0.03*log(w) -0.02*log(x) +0.05*log(y) +0.12*log(7*w+5*x + 2*y + z));
eq4: 1*z = (7*w+5*x+2*y+z) * (-0.16 + 0*log(w) - 0*log(x) - 0*log(y) +0.03*log(7*w+5*x + 2*y + z));
option show_stats 1;
option presolve 10;
option solver "/home/ali/ampl/ipopt"; # put your path here
option seed 1731;
# Initial solve
solve;
display w, x, y, z;
# Multistart
for {1..10} {
for {j in 1.._snvars}
let _svar[j] := Uniform(1, 50);
solve;
if (solve_result_num < 200) then {
display w, x, y, z;
}
}
If I only require that the variables are nonnegative, I get rubbish, for example
w = 2.39266e-11
x = 6.62678e-11
y = 1.57043e-24
z = 7.0842e-10
or
w = 1.09972e-12
x = 9.77807e-11
y = 3.36229e-21
z = 1.85441e-09
Numerically, these are indeed solutions, they satisfy the equations to a fairly high precision, although I am pretty sure it's not what you are looking for. This indicates issues with your model.
If I increase the lower bounds of the variables a bit:
var w := 14 >= 0.1;
var x := 15 >= 0.1;
var y := 10 >= 0.1;
var z := 100 >= 0.01;
I get, even with multistart, Ipopt 3.11.6: Converged to a locally infeasible point. Problem may be infeasible. This again indicates issues with your model equations.
I am afraid you will have to revise your model.
This won't fix the issues with your model equations but I would introduce new variables: a=log(w), b=log(x), c=log(y), d=log(z). Then w=exp(a) and so on. It has the advantage that the function evaluations won't fail due to negative arguments for the logarithm function.
I would probably also introduce a new variable for (7*w+5*x+2*y+z) just to make the equations more compact.
Neither of these new variables will solve the above issues with your model equations.
If it is really your first time using Mathematica, you might be better off with AMPL and IPOPT; these tools are custom-tailored for solving equations and optimization problems. I suggest you use the AMPL mailing list if you have question and not Stackoverflow; you will get better answers on the mailing list.
