Describe the bug 🐞
AbsNormSafeTerminationMode and AbsNormSafeBestTerminationMode accept an internalnorm, but their
stagnation check bypasses it:
du_norm = L2_NORM(cache.u_diff_cache)
This means that a user-provided norm controls the residual-based convergence checks but not the step-
stagnation checks.
This is problematic for distributed-memory solvers. An MPI-aware norm needs a global reduction. The
hard-coded L2_NORM instead evaluates a rank-local norm unless the distributed vector itself overloads
norm. Different ranks may then make different termination decisions and deadlock on the next collective
residual or linear-solver operation.
Expected behavior
A termination mode configured with internalnorm should use that norm consistently for all of its norm
evaluations, including the step-stagnation test.
In particular, I expect this line to use the mode’s configured norm:
du_norm = Utils.apply_norm(mode.internalnorm, cache.u_diff_cache)
rather than the hard-coded L2_NORM.
Minimal Reproducible Example 👇
using Test
using NonlinearSolveBase
using SciMLBase: NonlinearProblem, init
calls = Ref(0)
function counting_norm(x)
calls[] += 1
return 1.0
end
prob = NonlinearProblem((u, p) -> u, [1.0])
mode = AbsNormSafeBestTerminationMode(
counting_norm;
max_stalled_steps = 1,
)
cache = init(
prob,
mode,
[1.0],
[1.0];
abstol = 0.0,
reltol = 0.0,
)
# Two non-converged termination checks.
cache([1.0], [2.0], [1.0])
cache([1.0], [3.0], [2.0])
# Expected calls:
# 1 initial residual norm
# 2 residual norms in the two checks
# 2 step norms in the two stagnation checks
@test calls[] == 5Error & Stacktrace ⚠️
Test Failed at ...:...
Expression: calls[] == 5
Evaluated: 3 == 5Environment (please complete the following information):
- Output of
using Pkg; Pkg.status()
[8913a72c] NonlinearSolve v4.32.0
[be0214bd] NonlinearSolveBase v2.52.2
[0bca4576] SciMLBase v3.55.0
- Output of
using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
[47edcb42] ADTypes v1.24.0
[14f7f29c] AMD v0.5.4
[7d9f7c33] Accessors v0.1.45
[79e6a3ab] Adapt v4.7.1
[4fba245c] ArrayInterface v7.30.2
[70df07ce] BracketingNonlinearSolve v1.12.7
[38540f10] CommonSolve v0.2.14
[bbf7d656] CommonSubexpressions v0.3.1
[34da2185] Compat v4.18.1
[a33af91c] CompositionsBase v0.1.2
[2569d6c7] ConcreteStructs v0.2.8
[187b0558] ConstructionBase v1.6.0
[a8cc5b0e] Crayons v4.2.0
[9a962f9c] DataAPI v1.16.0
[e2d170a0] DataValueInterfaces v1.0.0
[8bb1440f] DelimitedFiles v1.9.1
[163ba53b] DiffResults v1.1.0
[b552c78f] DiffRules v1.16.0
[a0c0ee7d] DifferentiationInterface v0.7.21
[ffbed154] DocStringExtensions v0.9.5
[4e289a0a] EnumX v1.0.7
[f151be2c] EnzymeCore v0.8.21
[e2ba6199] ExprTools v0.1.11
[9aa1b823] FastClosures v0.3.2
[64ca27bc] FindFirstFunctions v3.3.0
[6a86dc24] FiniteDiff v2.33.0
[f6369f11] ForwardDiff v1.4.6
[069b7b12] FunctionWrappers v1.1.3
[77dc65aa] FunctionWrappersWrappers v1.13.0
[46192b85] GPUArraysCore v0.2.0
[3587e190] InverseFunctions v0.1.17
[92d709cd] IrrationalConstants v0.2.6
[82899510] IteratorInterfaceExtensions v1.0.0
[692b3bcd] JLLWrappers v1.8.0
[ba0b0d4f] Krylov v0.10.10
[2faa5264] LHLFactorization v2.2.2
[b964fa9f] LaTeXStrings v1.4.1
[87fe0de2] LineSearch v0.1.18
[7ed4a6bd] LinearSolve v5.17.7
[2ab3a3ac] LogExpFunctions v1.0.1
[e6f89c97] LoggingExtras v1.2.0
[1914dd2f] MacroTools v0.5.16
[bb5d69b7] MaybeInplace v0.1.8
[77ba4419] NaNMath v1.1.4
[8913a72c] NonlinearSolve v4.32.0
[be0214bd] NonlinearSolveBase v2.52.2
[5959db7a] NonlinearSolveFirstOrder v2.9.1
[9a2c21bd] NonlinearSolveQuasiNewton v1.15.3
[26075421] NonlinearSolveSpectralMethods v1.8.3
[bac558e1] OrderedCollections v2.0.1
[d236fae5] PreallocationTools v1.7.1
[aea7be01] PrecompileTools v1.3.4
[21216c6a] Preferences v1.6.0
[08abe8d2] PrettyTables v3.4.8
[0c0d3e7f] PureKLU v1.6.0
[3cdcf5f2] RecipesBase v1.3.4
[731186ca] RecursiveArrayTools v4.5.1
[189a3867] Reexport v1.2.2
[9fe22ead] RespecializeParams v1.3.0
[7e49a35a] RuntimeGeneratedFunctions v0.5.26
[0bca4576] SciMLBase v3.55.0
[19f34311] SciMLJacobianOperators v0.1.19
[a6db7da4] SciMLLogging v2.1.0
[c0aeaf25] SciMLOperators v1.30.1
[431bcebd] SciMLPublic v1.3.0
[53ae85a6] SciMLStructures v1.10.5
[efcf1570] Setfield v1.1.2
[727e6d20] SimpleNonlinearSolve v2.14.5
[ed01d8cd] Sobol v1.5.0
[a57abbd0] SparseColumnPivotedQR v2.1.8
[276daf66] SpecialFunctions v2.9.0
[1e83bf80] StaticArraysCore v1.4.4
[10745b16] Statistics v1.11.5
⌅ [892a3eda] StringManipulation v0.5.0
[2efcf032] SymbolicIndexingInterface v0.3.55
[3783bdb8] TableTraits v1.0.1
[bd369af6] Tables v1.14.0
[a759f4b9] TimerOutputs v1.2.2
[1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
[856f044c] MKL_jll v2025.2.0+0
[efe28fd5] OpenSpecFun_jll v0.5.6+0
[1317d2d5] oneTBB_jll v2022.3.0+0
[0dad84c5] ArgTools v1.1.2
[56f22d72] Artifacts v1.11.0
[2a0f44e3] Base64 v1.11.0
[ade2ca70] Dates v1.11.0
[8ba89e20] Distributed v1.11.0
[f43a241f] Downloads v1.7.0
[7b1f6079] FileWatching v1.11.0
[9fa8497b] Future v1.11.0
[b77e0a4c] InteractiveUtils v1.11.0
[ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
[4af54fe1] LazyArtifacts v1.11.0
[b27032c2] LibCURL v1.0.0
[76f85450] LibGit2 v1.11.0
[8f399da3] Libdl v1.11.0
[37e2e46d] LinearAlgebra v1.13.0
[56ddb016] Logging v1.11.0
[d6f4376e] Markdown v1.11.0
[a63ad114] Mmap v1.11.0
[ca575930] NetworkOptions v1.3.0
[44cfe95a] Pkg v1.13.0
[de0858da] Printf v1.11.0
[3fa0cd96] REPL v1.11.0
[9a3f8284] Random v1.11.0
[ea8e919c] SHA v1.0.0
[9e88b42a] Serialization v1.11.0
[6462fe0b] Sockets v1.11.0
[2f01184e] SparseArrays v1.13.0
[f489334b] StyledStrings v1.11.0
[fa267f1f] TOML v1.0.3
[a4e569a6] Tar v1.10.0
[cf7118a7] UUIDs v1.11.0
[4ec0a83e] Unicode v1.11.0
[e66e0078] CompilerSupportLibraries_jll v1.5.5+2
[deac9b47] LibCURL_jll v8.18.0+1
[e37daf67] LibGit2_jll v1.9.1+0
[29816b5a] LibSSH2_jll v1.11.103+0
[14a3606d] MozillaCACerts_jll v2026.8.13
[4536629a] OpenBLAS_jll v0.3.30+0
[05823500] OpenLibm_jll v0.8.7+0
[458c3c95] OpenSSL_jll v3.5.6+0
[efcefdf7] PCRE2_jll v10.46.0+0
[bea87d4a] SuiteSparse_jll v7.10.1+0
[83775a58] Zlib_jll v1.3.1+2
[3161d3a3] Zstd_jll v1.5.7+1
[8e850b90] libblastrampoline_jll v5.15.0+0
[8e850ede] nghttp2_jll v1.67.1+0
[3f19e933] p7zip_jll v17.8.2+0
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
Julia Version 1.13.0
Commit d1c37793dd2 (2026-09-09 19:00 UTC)
Build Info:
Official https://julialang.org release
Platform Info:
OS: macOS (arm64-apple-darwin25.6.0)
CPU: 16 × Apple M4 Max
WORD_SIZE: 64
LLVM: libLLVM-20.1.8 (ORCJIT, apple-m4)
GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 16 virtual cores)
Additional context
There is a related API question: solve(...; internalnorm=...) does not propagate that norm into the
automatically constructed default termination condition. The default root-finding termination mode uses
maximum(abs, residual), i.e. a local L∞ norm.
I am less certain whether that part is intended design or a bug. The issue above is independent: even
when a user explicitly constructs a termination mode with a custom norm, its stagnation path
currently ignores that norm.
Describe the bug 🐞
AbsNormSafeTerminationMode and AbsNormSafeBestTerminationMode accept an internalnorm, but their
stagnation check bypasses it:
This means that a user-provided norm controls the residual-based convergence checks but not the step-
stagnation checks.
This is problematic for distributed-memory solvers. An MPI-aware norm needs a global reduction. The
hard-coded L2_NORM instead evaluates a rank-local norm unless the distributed vector itself overloads
norm. Different ranks may then make different termination decisions and deadlock on the next collective
residual or linear-solver operation.
Expected behavior
A termination mode configured with internalnorm should use that norm consistently for all of its norm
evaluations, including the step-stagnation test.
In particular, I expect this
lineto use the mode’s configured norm:rather than the hard-coded L2_NORM.
Minimal Reproducible Example 👇
Error & Stacktrace⚠️
Environment (please complete the following information):
using Pkg; Pkg.status()using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)versioninfo()Additional context
There is a related API question: solve(...; internalnorm=...) does not propagate that norm into the
automatically constructed default termination condition. The default root-finding termination mode uses
maximum(abs, residual), i.e. a local L∞ norm.
I am less certain whether that part is intended design or a bug. The issue above is independent: even
when a user explicitly constructs a termination mode with a custom norm, its stagnation path
currently ignores that norm.