What is the default method used by FindMinimum
with constraints?
The documentation says:
"Currently, the only method available for constrained optimization is the interior point algorithm"
However, a random example gives different results for the Method -> Automatic
and Method -> "InteriorPoints"
:
Reap[
FindMinimum[
{x^2 + y^2,
(x - 1)^2 + 2 (y - 1)^2 > 5},
{{x, 4}, {y, 4}},
Method -> Automatic,
StepMonitor :> Sow[{x^2 + y^2, x, y}]
]
]
Reap[
FindMinimum[
{x^2 + y^2,
(x - 1)^2 + 2 (y - 1)^2 > 5},
{{x, 4}, {y, 4}},
Method -> "InteriorPoint",
StepMonitor :> Sow[{x^2 + y^2, x, y}]
]
]
The above code yields the same final solution but the steps taken are different for each, which suggests that the interior points method is not actually the default one in this case.
The same question has been asked here and here
So what is the exact method being used when Method -> Automatic
is specified?