[Edited 20:02 for concision]

Problem statement: NArgMin correctly obeys constraints when evaluating locally (on $Version = "11.3.0 for Mac OS X x86 (64-bit) (March 7, 2018)"), but when the cloud deployed version of the function does not correctly obey the constraints and returns different results.

Minimal broken example:

test2[input_String] := Module[
  {x = ToExpression[input],
   m = {{0.75`, 0, 0}, {0.38`, 5.84`, 0}, {1, 1, 1}},
   v1, v2, v3},
    Norm[m.{v1, v2, v3} - Append[x, 1] ],
    Element[{v1, v2, v3}, Cuboid[{0, 0, 0}, {1, 1, 1}]],
    AccuracyGoal -> 0.0001,
    PrecisionGoal -> 0.0001]
   // ToString

example = "{0.0919614, 0.0926934}"
test2[example] (*correctly returns "{0.122615, 0.00789377, 0.869491}"*)

In contrast, when deployed to cloud, a different result is returned which violates the positivity constrain on the arguments.

api = APIFunction[{"input" -> String}, test2[#input] &]
deployedFunction2 = CloudDeploy[ api, Permissions -> "Public"]

URLExecute[deployedFunction2, {"input" -> example}] (*incorrectly returns "{0.405362, -0.00654954, 0.593471}", which violates the region constraint in NArgMin*)

Conclusion: I'm puzzled why the cloud version of the NArgMin call returns the wrong result, and does not correctly obey the provided constraints, whereas the local version works OK. What am I missing here?

  • $\begingroup$ (I reduced this down to an even smaller example) $\endgroup$ – Joshua Schrier Jun 6 at 1:05

The basic issue is that you're misinterpreting the meaning of the AccuracyGoal and PrecisionGoal. For example:

WolframLanguageData["AccuracyGoal", "PlaintextUsage"]

"AccuracyGoal is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result."

So, using AccuracyGoal->.0001 means that you'll accept an answer with basically 0 digits of accuracy, or in other words, basically any answer is fine.

As for the difference between M11.3 and the cloud, the cloud uses M12, and there's been a change in behavior for this edge case.

  • $\begingroup$ Aha! AccuracyGoal and PrecisionGoal set number of digits, not values. Confirmed that this works correctly. Thanks for your help. $\endgroup$ – Joshua Schrier Jun 6 at 18:02

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