# What is this error when doing Plot[ArgMin[Norm[…,p]],…]?

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,
p-0,Im[Abs[-5+x]^p+Abs[x]^p+Abs[1+x]^p+Abs[3+x]^p]-0}
must be a list of equalities or real-valued functions.


The plot itself seems to be OK

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

• What happens if you add Exclusions -> None? – J. M. is away Jan 5 at 4:53
• @J.M.iscomputer-less Aha the error is gone then. The plot is the same. Could you explain this, in an answer? – მამუკა ჯიბლაძე Jan 5 at 4:54
• Before anything else: what version and OS is this? – J. M. is away Jan 5 at 4:54
• @J.M.iscomputer-less 11.0.1.0 on Windows 10 – მამუკა ჯიბლაძე Jan 5 at 4:55
• I do not get an error message with v11.3 on a Mac. – 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},