In[]:=
fx[xup_,yup_,xsub_,y_,xpar_]:=Sin[xsub+xparxup+yup(xpar+y)]​​fy[xup_,yup_,ysub_,x_,ypar_]:=Cos[ysub+yparyup+xup(ypar+x)]​​gx[xdown_,ydown_,y_,xE_,xpar_]:=xpar+(xdown(ydown-y)^2-xparxE)^2​​gy[xdown_,ydown_,x_,xE_,ypar_]:=ypar+(ydown(xdown-x)^2-yparxE)^2​​x1par[x1_,y1_,y2_]:=NArgMin[gx[x1,y1,y2,xE1,x1p]/.xE11,x1p]​​y1par[x1_,y1_,x2_]:=NArgMin[gy[x1,y1,x2,xE2,y1p]/.xE20.5,y1p]​​rule1=NSolve[{x1==NMinValue[fx[x2,y2,xsub,y1,x1par[x1,y1,x2]],xsub],​​y1==NMinValue[fy[x2,y2,ysub,x1,y1par[x1,y1,y2]],ysub],​​x2==NMinValue[gx[x1,y1,y2,xE1,x1p]/.xE11,x1p],​​ y2==NMinValue[gy[x1,y1,x2,xE2,y1p]/.xE20.5,y1p]​​ },​​{x1,y1,x2,y2},Reals]
NArgMin
:The function value -0.829053+
2
0.829053+x1
2
(-x2+y1)

is not a number at {x1p} = {-0.829053}.
NArgMin
:The function value -0.829053+
2
0.829053+x1
2
(-x2+y1)

is not a number at {x1p} = {-0.829053}.
NArgMin
:The function value -0.829053+
2
0.829053+x1
2
(-x2+y1)

is not a number at {x1p} = {-0.829053}.
General
:Further output of NArgMin::nnum will be suppressed during this calculation.
NMinValue
:The function value -Sin0.829053-x2NArgMinx1p+
2
Plus[2]
,x1p-y2(y1+NArgMin[x1p+Power[2],x1p]) is not a number at {xsub} = {-0.829053}.
NMinValue
:The function value Cos0.829053-y2NArgMiny1p+
2
(Times[2]+Times[2])
,y1p-x2x1+NArgMiny1p+
2
Plus[2]
,y1p is not a number at {ysub} = {-0.829053}.
NMinValue
:The function value -0.829053+
2
0.829053+x1
2
(y1-y2)

is not a number at {x1p} = {-0.829053}.
General
:Further output of NMinValue::nnum will be suppressed during this calculation.
​
In[]:=
x1par[1,1,2]
Out[]=
0.5
In[]:=
NMinValue[fx[2,3,xsub,1,x1par[1,1,2]],xsub]
Out[]=
-1.
In[]:=
NArgMin[gx[1,2,3,xE1,x1p]/.xE11,x1p]
Out[]=
0.5
In[]:=
x2=NMinimize[gx[x1,y1,y2,xE1,x1p]/.{xE11,x11,y11,y20.4},x1p]
Out[]=
{0.11,{x1p-0.14}}
In[]:=
?gx
Out[]=
Symbol
Global`gx
Definitions
gx[xdown_,ydown_,y_,xE_,xpar_]:=xpar+
2
(xdown
2
(ydown-y)
-xparxE)
Full Name
Global`gx
​
In[]:=
gx[xdown_,ydown_,y_,xE_,xpar_]:=xpar+(xdown(ydown-y)^2-xparxE)^2;
In[]:=
x1par=x1p/.Last[NMinimize[gx[1,1,0.4`,1,x1p],x1p]]
Out[]=
-0.14
In[]:=
fy[xup_,yup_,ysub_,x_,ypar_]:=Cos[ysub+yparyup+xup/(ypar+x)];​​y1=First[NMinimize[fy[X2,y2,ysub,x1,y1par]/.{X21,y21,x10.3,y1par-0.2},ysub]]
Out[]=
-1.