I wish to resolve a number of equations so I believed utilizing `NMinimize`

. The essential concept is that you probably have a number of equations with a number of variables :

$$left{start{break up}&f(x,y,z)=0 &g(x,y,z)=0 & h(x,y,z)=0end{break up}proper.$$

You could find the answer by minimizing : $|f(x,y,z)|+|g(x,y,z)|+|h(x,y,z)|$.

So that is what I am attempting to do right here on this code with the capabilities `p[a0, b0, c, d, x, y] - p[a0, b0, c, d, w, z]`

,`Hx[a0, b0, c, d, x, y] - Hx[a0, b0, c, d, w, z]`

,

`Hy[a0, b0, c, d, x, y] - Hy[a0, b0, c, d, w, z]`

.

My drawback is that after I’m altering somewhat bit the situation : `z>...`

the outcome turns into totally different.

Right here is the introduction to the `NMinimize`

:

```
a0=0.0748294;
b0=0.629316;
h[x_, y_] =
a*x*Log[x] + b*(1 - x - y)*Log[1 - x - y] + c*y*Log[y] - x^2 - d*x*y;
"------------------------------"
Hx[x_, y_] = D[h[x, y], x];
Hy[x_, y_] = D[h[x, y], x];
hxx[x_, y_] = D[h[x, y], x, x];
hxy[x_, y_] = D[h[x, y], x, y];
hyy[x_, y_] = D[h[x, y], y, y];
det[x_, y_] = Det[{{hxx[x, y], hxy[x, y]}, {hxy[x, y], hyy[x, y]}}];
p[x_, y_] = h[x, y] - x*Hx[x, y] - y*Hy[x, y];
h[a_, b_, c_, d_, x_, y_] = h[x, y];
p[a_, b_, c_, d_, x_, y_] = p[x, y];
Hx[a_, b_, c_, d_, x_, y_] = Hx[x, y];
Hy[a_, b_, c_, d_, x_, y_] = Hy[x, y];
det[a_, b_, c_, d_, x_, y_] = det[x, y];
x = 0.001;
y = 0.001;
w = 0.4;
```

And listed below are the a number of `NMinimize`

altering somewhat bit the situation. As you possibly can see, the situation I am altering is `z>0.2`

,`z>0.3`

,`z>0.4`

. And as you possibly can see all the outcomes give $z>0.4$ so none of them contradicts any of the circumstances.

```
sol = NMinimize[{Abs[p[a0, b0, c, d, x, y] - p[a0, b0, c, d, w, z]] +
Abs[Hx[a0, b0, c, d, x, y] - Hx[a0, b0, c, d, w, z]] +
Abs[Hy[a0, b0, c, d, x, y] - Hy[a0, b0, c, d, w, z]],
c > 0 && d > 0 && z > 0.2 && z < 1 - w &&
det[a0, b0, c, d, w, z] > 0}, {c, d, z}, Reals,
AccuracyGoal -> 20, PrecisionGoal -> 22, MaxIterations -> 1000]
sol = NMinimize[{Abs[p[a0, b0, c, d, x, y] - p[a0, b0, c, d, w, z]] +
Abs[Hx[a0, b0, c, d, x, y] - Hx[a0, b0, c, d, w, z]] +
Abs[Hy[a0, b0, c, d, x, y] - Hy[a0, b0, c, d, w, z]],
c > 0 && d > 0 && z > 0.3 && z < 1 - w &&
det[a0, b0, c, d, w, z] > 0}, {c, d, z}, Reals,
AccuracyGoal -> 20, PrecisionGoal -> 22, MaxIterations -> 1000]
sol = NMinimize[{Abs[p[a0, b0, c, d, x, y] - p[a0, b0, c, d, w, z]] +
Abs[Hx[a0, b0, c, d, x, y] - Hx[a0, b0, c, d, w, z]] +
Abs[Hy[a0, b0, c, d, x, y] - Hy[a0, b0, c, d, w, z]],
c > 0 && d > 0 && z > 0.4 && z < 1 - w &&
det[a0, b0, c, d, w, z] > 0}, {c, d, z}, Reals,
AccuracyGoal -> 20, PrecisionGoal -> 22, MaxIterations -> 1000]
```

The outcomes :

```
-> {0., {c -> 0.584662, d -> 2.09663, z -> 0.486347}}
-> {1.94289*10^-16, {c -> 0.560407, d -> 2.26232, z -> 0.507207}}
-> {1.8735*10^-16, {c -> 0.114809, d -> 3.31333, z -> 0.571615}}
```

As you possibly can see they’re all totally different. How can I do to seek out the precise outcome ?