StepMonitor variable replacement depends on presence of constraint in FindMinimum

Question

Contrast the results of StepMonitor between the two calls to FindMinimum, which differ only in that the second contains a constraint on the argument to the objective function.

ClearAll[f, wrap, x];
f[x_] := (x)^2;
wrap = {x};
FindMinimum[{f[Sequence @@ wrap]}, x, StepMonitor :> Print["step to ", wrap]]
FindMinimum[{f[Sequence @@ wrap], x > 1}, x, StepMonitor :> Print["step to ", wrap]]

(*
step to {0.}
{0.,{x->0.}}
step to {x}
step to {x}
step to {x}
step to {x}
step to {x}
step to {x}
{1.,{x->1.}}
*)

The second version prints out {x} instead of the current guess of x. I need to be able to print out the current guess of the argument at each step without abandoning the constraint.

You might be wondering why I use wrap at all. The answer is that this is a minimal not working example of an issue I ran into for which the objective function is a function of several arguments, some of which are scalars with constraints, and some of which are variable length lists without constraints. I need to minimize the function over all of the arguments, and I can't hard code the arguments of the variable length lists into StepMonitor.

How could I alter my code so that StepMonitor will print out the current value of the arguments over which FindMinimum is searching without hard coding the variable names?

Answer 1

Use With to inject the value of wrap into your code (I also used f @@ wrap instead of your f[Sequence @@ wrap]):

f[x_] := x^2
With[{wrap = {x}},
    FindMinimum[{f@@wrap}, x, StepMonitor:>Print["step to ", wrap]]
]

step to {0.}

{0., {x -> 0.}}

compared to:

With[{wrap = {x}},
    FindMinimum[{f@@wrap, x>1}, x, StepMonitor:>Print["step to ", wrap]]
]

step to {2.}

step to {1.01}

step to {1.00986}

step to {1.00017}

step to {1.}

step to {1.}

{1., {x -> 1.}}