When doing

Plot[ArgMin[Norm[x - {-3, -1, 0, 5}, p], x], {p, 1, 3}]

I get this error message:

Plot::exclul: {(Abs[-5+x]^p+Abs[x]^p+Abs[1+x]^p+Abs[3+x]^p)-0,(3+x)-0,(1+x)-0,x-0,(-5+x)-0,
 must be a list of equalities or real-valued functions.

The plot itself seems to be OK

enter image description here

-- although I am not sure because of this error. What caused it?

  • 1
    $\begingroup$ What happens if you add Exclusions -> None? $\endgroup$ – J. M. is away Jan 5 at 4:53
  • $\begingroup$ @J.M.iscomputer-less Aha the error is gone then. The plot is the same. Could you explain this, in an answer? $\endgroup$ – მამუკა ჯიბლაძე Jan 5 at 4:54
  • $\begingroup$ Before anything else: what version and OS is this? $\endgroup$ – J. M. is away Jan 5 at 4:54
  • 1
    $\begingroup$ @J.M.iscomputer-less on Windows 10 $\endgroup$ – მამუკა ჯიბლაძე Jan 5 at 4:55
  • 2
    $\begingroup$ I do not get an error message with v11.3 on a Mac. $\endgroup$ – Bob Hanlon Jan 5 at 4:59

This is a bug that seems to have been resolved in version 11.1, and is related to the exclusion detection functionality used by Mathematica to detect discontinuities. (The presence of Abs[] in the function being analyzed is what triggered the exclusion detection.)

Since you know that the function is continuous in your range of interest, just add Exclusions -> None:

Plot[ArgMin[Norm[x - {-3, -1, 0, 5}, p], x], {p, 1, 3}, 
     Exclusions -> None]

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