It doesn't work at all for ParametricIPOPTMinimize
In[21]:= Needs["IPOPTLink`"]
In[22]:= f[x_, y_] := x Sin[10 x] y ^2 Cos[5 y]
In[23]:= ipts = RandomPoint[Disk[{-1, -1}], 1000];
In[24]:= pf =
ParametricIPOPTMinimize[
f[x, y], {x, y}, {x0,
y0}, {{-2, 0}, {-2, 0}}, {(x + 1)^2 + (y + 1)^2}, {{0, 1}}, {x0,
y0}]
Out[24]= ParametricFunction[ <> ]
In[25]:= AbsoluteTiming[sols = Map[pf[Sequence @@ #] &, ipts];]
Out[25]= {4.55567, Null}
In[28]:= IPOPTMinValue[sols[[1]]]
Out[28]= -1.82848
In[30]:= sols[[1]]
Out[30]= IPOPTData[1]
In[27]:= AbsoluteTiming[
solsp = ParallelMap[pf[Sequence @@ #] &, ipts];]
Out[27]= {0.330978, Null}
In[31]:= solsp[[1]]
Out[31]= ParametricFunction[2,
Internal`Bag[{Hold[
ParametricIPOPTMinimize[x y^2 Cos[5 y] Sin[10 x], {x, y},
ParametricIPOPTData[
1, {x y^2 Cos[5 y] Sin[10 x], {(1 + x)^2 + (1 + y)^2}, {{0,
1}}, {x, y}, {{-2, 0}, {-2, 0}}, {x0,
y0}, {{1, 1}, {1, 2}}, {{1, 1}, {2, 1}, {2,
2}}, {"nlp_lower_bound_inf" -> -1.*10^19,
"nlp_upper_bound_inf" -> 1.*10^19}, Automatic, True,
IPOPTMinimize}, {x0, y0}]]]}, 1, 1], 0,
1, {{x0$6679, y0$6680},
System`Utilities`HashTable[
1, {{y0$6680, y0}, {x0$6679, x0}}], {}, {}, {},
None}, {NDSolve`base$6681,
ParametricIPOPTData[
1, {x y^2 Cos[5 y] Sin[10 x], {(1 + x)^2 + (1 + y)^2}, {{0,
1}}, {x, y}, {{-2, 0}, {-2, 0}}, {x0$6679,
y0$6680}, {{1, 1}, {1, 2}}, {{1, 1}, {2, 1}, {2,
2}}, {"nlp_lower_bound_inf" -> -1.*10^19,
"nlp_upper_bound_inf" -> 1.*10^19}, Automatic, True,
IPOPTMinimize}, {x0$6679, y0$6680}]}][-1.10076, -1.53568]