Bug in NMaximize in 12.2?

Question

Bug introduced in 12.2, Fixed in 12.3

Something changed in NMaximze in v12.2:

NMaximize[E^(-x^2) - 1, x]
(* {(-1 + E^#1)[0.], {x -> 0.}} *)

v12.1 works as expected:

NMaximize[E^(-x^2) - 1, x]
(* {0., {x -> 0.}} *)

as does Maximize in v12.2:

Maximize[E^(-x^2) - 1, x]
(* {0, {x -> 0}} *)

Do you all agree this is a bug? Any ideas on a workaround?

$Version
(* "12.2.0 for Mac OS X x86 (64-bit) (December 12, 2020)" *)

Consider: NMaximize[E^(-x^2.) - 1, x] This seems to return a reasonable numerical answer, so maybe this narrows down the location of the bug. — bill s, Commented May 1, 2021 at 22:56
This is fixed in the 12.3 prerelease version 12.3.0 for Mac OS X x86 (64-bit) (April 13, 2021) — Rohit Namjoshi, Commented May 2, 2021 at 3:05
Here's a cute fix: MapAt[Function, NMaximize[E^(-x^2) - 1, x], {1, 0}]. Not as good as Optimization`UseConvexMinimize = False though. (Not nearly, since it fails whenever NMaximize succeeds.) BTW, @bills, the convex minimizer rejects the problem with the exponent 2. as "not transformable," and NMaximize falls back onto the old automatic method. — Michael E2, Commented May 2, 2021 at 16:13
Since this is for a shared package, I used If[$VersionNumber==12.2, Block[{Optimization`UseConvexMinimize=False}, ...] because you can never be sure what version of Mathematica people will be using. — Chris K, Commented May 2, 2021 at 16:56

Michael E2 · Accepted Answer · 2021-05-01 19:30:51Z

13

It seems (clearly!) to be a bug in the preprocessing for the new convex optimizer. Use one of the other methods (e.g. "DifferentialEvolution"):

Trace[
 NMaximize[E^(-x^2) - 1, x],
 _Optimization`MinimizationProblem,
 TraceForward -> True,
 TraceInternal -> True
 ]

Workaround:

NMaximize[E^(-x^2) - 1, x, Method -> "DifferentialEvolution"]

(*  {0., {x -> -5.45643*10^-9}}  *)

Alternatively, you can turn off the convex minimizer:

Block[{Optimization`UseConvexMinimize = False},
 NMinimize[-(E^(-x^2) - 1), x]
 ]

(*   {0., {x -> -5.45643*10^-9}}  *)

answered May 1, 2021 at 19:23

Michael E2

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$\begingroup$ Maybe just a missing & in there. Thanks for the workarounds and I'll report to WRI. $\endgroup$
– Chris K
Commented May 1, 2021 at 19:37
$\begingroup$ @ChrisK Seems to be the added constant ("vertical shift") that triggers the bug. Also occurs here: NMinimize[1 + Log[1 + x^2], x]. $\endgroup$
– Michael E2
Commented May 1, 2021 at 19:52
4

$\begingroup$ This is fixed in the 12.3 prerelease version 12.3.0 for Mac OS X x86 (64-bit) (April 13, 2021) $\endgroup$
– Rohit Namjoshi
Commented May 2, 2021 at 3:07

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