I'm trying to monitor the progress of FindMinimum[] using StepMonitor. I'd specifically like to have the code print out the value of the objective function and the variable values. For example,

FindMinimum[{objF = objFunc[x, y], x >0, y>0}, {{x, 1}, {y, 1}},
  StepMonitor:> {Print[{objF, x, y}]}

where I've been careful to restrict calculation of objFunc[] to only the cases where it has numerical values for x and y. That is,

 objF[x_?NumericQ, y_?NumericQ] := Module[{}, ....]

When I try running the FindMinimum[] above, my output looks like this.

 {objFunc[x, y], 0.235, 1.875}
 {objFunc[x, y], 0.244, 1.654}

I've tried using

  • StepMonitor:> {Print[{Evaluate[objF], x, y}]}
  • StepMonitor:> {Print[{objF/.{x->x, y->y}, x, y}]}
  • StepMonitor:> {Print[{objF/.{Hold[x]->x, Hold[y]->y}, x, y}]}

But none of them give the desired results.

Confusingly, to me anyway, EvaluationMonitor behaves the way I expect. That is,

EvaluationMonitor:> {Print[{objF, x, y}]}


{33.456, 1.000, 1.000}
{32.456, 0.235, 1.875}
{31.555, 0.244, 1.654}

How do I solve this issue?

ps. Perhaps these problems would be solved using Reap[] and Sow[], but I'd like to monitor the progress of the optimization in real time, not after the fact.


1 Answer 1


It is because FindMinimum has the attribute HoldAll and you need to inject the expression objFunc[x, y] or objF[x, y] (it appears both ways in the OP currently) into the StepMonitor code. Injection can be accomplished with With. What appears to happen is this:

  • At each step, any appearances of x and y in the literal code {objF, x, y} passed to StepMonitor are replaced by their numeric values at the current step.
  • The resulting expression is evaluated. At this point the symbol objF evaluates to objFunc[x, y], which appears as is when printed, since objFunc does not evaluate on symbolic input.

I could show how on a minimal working example, but there isn't one.


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