NonlinearLeastSquares does not converge to or accept the correct minimum

[hstrey]

Describe the bug 🐞

It seems that the NonLinearLeastSquaresProblem with subsequent solve (I used the default solver that tries all NLLSQ solvers) , does not converge to the correct minimum (or potentially does not accept it). As you can see below non of the solvers properly converges, even though this is a really simple Non-linear least squares problem. I tried it on more complicated fit functions and it has the same problem. Maybe I am missing some settings, but it makes no sense that it finds a better solution if the initial value is further from the ground-truth.

Expected behavior

It should converge

We use a NonLinearLeastSquaresProblem to get the parameters of a line. Instead of properly estimating the parameters it returns the initial conditions. LsqFit returns the correct values, which uses the LevenbergMarquardt algorithm (one of the solvers that is used by the default polysolver)

Minimal Reproducible Example 👇

using NonlinearSolve, LsqFit, Random, ForwardDiff

Random.seed!(123)

x = collect(0:0.1:10)

line_fct(x,p) = p[1] .+ p[2] .* x

y_line = line_fct(x,[1,3])
y_line_n = line_fct(x,[1,3]) + randn(length(x))

res(β,(x,y)) = line_fct(x,β) .- y
prob = NonlinearLeastSquaresProblem(res, [1,3], p=(x,y_line_n))
sol = solve(prob; maxiters =1000, show_trace = Val(true))

prob = NonlinearLeastSquaresProblem(res, [1,5], p=(x,y_line_n))
sol = solve(prob; maxiters =1000, show_trace = Val(true))

# LsqFit gives the correct parameter values with the initial conditions that failed before
fit = curve_fit(line_fct,x,y_line_n,[1.0,3.0])
fit.param
2-element Vector{Float64}:
 0.8489074606311343
 3.0226579109194747

Error & Stacktrace ⚠️

output for the first example:

Algorithm: GaussNewton(
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.29278542e+00          1.52781990e-01
...
32              9.29278542e+00          2.43036904e-16      
33              9.32421225e+00          1.34966536e-16      
Final           9.32421225e+00      
----------------------      

Algorithm: LevenbergMarquardt(
    trustregion = LevenbergMarquardtTrustRegion(
        β_uphill = 1.0
    ),
    descent = DampedNewtonDescent(
        initial_damping = 1.0,
        damping_fn = LevenbergMarquardtDampingFunction(
            increase_factor = 2.0,
            decrease_factor = 3.0,
            min_damping = 1.0e-8
        )
    ),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{true}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.31582904e+00          2.34698992e-02      
...   
41              9.29278542e+00          7.75352333e-17      
42              9.32421225e+00          4.43184381e-16      
Final           9.32421225e+00      
----------------------      

Algorithm: TrustRegion(
    trustregion = GenericTrustRegionScheme(
        method = __Simple(),
        step_threshold = 1//10000,
        shrink_threshold = 1//4,
        shrink_factor = 1//4,
        expand_factor = 2//1,
        expand_threshold = 3//4,
        max_trust_radius = 0//1,
        initial_trust_radius = 0//1
    ),
    descent = Dogleg(
        newton_descent = NewtonDescent(),
        steepest_descent = SteepestDescent()
    ),
    max_shrink_times = 32,
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.29278542e+00          1.52781990e-01      
... 
32              9.29278542e+00          0.00000000e+00      
33              9.32421225e+00          0.00000000e+00      
Final           9.32421225e+00      
----------------------      

Algorithm: GaussNewton(
    linesearch = BackTracking(
        c_1 = 0.0001,
        ρ_hi = 0.5,
        ρ_lo = 0.1,
        order = Val{3}(),
        maxstep = Inf,
        initial_alpha = true,
        maxiters = 1000
    ),
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.29278542e+00          1.52781990e-01      
...
32              9.29278542e+00          2.43036904e-16      
33              9.32421225e+00          1.34966536e-16      
Final           9.32421225e+00      
----------------------      

Algorithm: TrustRegion(
    trustregion = GenericTrustRegionScheme(
        method = __Bastin(),
        step_threshold = 1//10000,
        shrink_threshold = 1//4,
        shrink_factor = 1//4,
        expand_factor = 2//1,
        expand_threshold = 3//4,
        max_trust_radius = 0//1,
        initial_trust_radius = 0//1
    ),
    descent = Dogleg(
        newton_descent = NewtonDescent(),
        steepest_descent = SteepestDescent()
    ),
    max_shrink_times = 32,
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.29278542e+00          1.52781990e-01      
...
32              9.29278542e+00          0.00000000e+00      
33              9.32421225e+00          0.00000000e+00      
Final           9.32421225e+00      
----------------------      

Algorithm: LevenbergMarquardt(
    trustregion = LevenbergMarquardtTrustRegion(
        β_uphill = 1.0
    ),
    descent = GeodesicAcceleration(
        descent = DampedNewtonDescent(
            initial_damping = 1.0,
            damping_fn = LevenbergMarquardtDampingFunction(
                increase_factor = 2.0,
                decrease_factor = 3.0,
                min_damping = 1.0e-8
            )
        ),
        finite_diff_step_geodesic = 0.1,
        α = 0.75
    ),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{true}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               9.32421225e+00          0.00000000e+00      
1               9.31582904e+00          2.34698992e-02      
...
113             9.29278542e+00          0.00000000e+00      
114             9.32421225e+00          2.39871929e-16      
Final           9.32421225e+00      
----------------------      
retcode: Stalled
u: 2-element Vector{Float64}:
 1.0
 3.0

output for the second example:

Algorithm: GaussNewton(
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               9.29278542e+00          1.98310632e+00      
...   
32              9.29278542e+00          2.43036904e-16      
33              9.29278542e+00          1.34966536e-16      
Final           9.29278542e+00      
----------------------      

Algorithm: LevenbergMarquardt(
    trustregion = LevenbergMarquardtTrustRegion(
        β_uphill = 1.0
    ),
    descent = DampedNewtonDescent(
        initial_damping = 1.0,
        damping_fn = LevenbergMarquardtDampingFunction(
            increase_factor = 2.0,
            decrease_factor = 3.0,
            min_damping = 1.0e-8
        )
    ),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{true}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               4.80497109e+01          3.19080865e+00      
...     
41              9.29278542e+00          7.75352333e-17      
42              9.29278542e+00          4.43184381e-16      
Final           9.29278542e+00      
----------------------      

Algorithm: TrustRegion(
    trustregion = GenericTrustRegionScheme(
        method = __Simple(),
        step_threshold = 1//10000,
        shrink_threshold = 1//4,
        shrink_factor = 1//4,
        expand_factor = 2//1,
        expand_threshold = 3//4,
        max_trust_radius = 0//1,
        initial_trust_radius = 0//1
    ),
    descent = Dogleg(
        newton_descent = NewtonDescent(),
        steepest_descent = SteepestDescent()
    ),
    max_shrink_times = 32,
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               9.29278542e+00          1.98310632e+00      
2               9.29278542e+00          0.00000000e+00      
...      
32              9.29278542e+00          0.00000000e+00      
33              9.29278542e+00          0.00000000e+00      
Final           9.29278542e+00      
----------------------      

Algorithm: GaussNewton(
    linesearch = BackTracking(
        c_1 = 0.0001,
        ρ_hi = 0.5,
        ρ_lo = 0.1,
        order = Val{3}(),
        maxstep = Inf,
        initial_alpha = true,
        maxiters = 1000
    ),
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               9.29278542e+00          1.98310632e+00      
2               9.29278542e+00          3.41389753e-15      
...
32              9.29278542e+00          2.43036904e-16      
33              9.29278542e+00          1.34966536e-16      
Final           9.29278542e+00      
----------------------      

Algorithm: TrustRegion(
    trustregion = GenericTrustRegionScheme(
        method = __Bastin(),
        step_threshold = 1//10000,
        shrink_threshold = 1//4,
        shrink_factor = 1//4,
        expand_factor = 2//1,
        expand_threshold = 3//4,
        max_trust_radius = 0//1,
        initial_trust_radius = 0//1
    ),
    descent = Dogleg(
        newton_descent = NewtonDescent(),
        steepest_descent = SteepestDescent()
    ),
    max_shrink_times = 32,
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               5.82631937e+01          1.00000000e+00      
...
33              9.29278542e+00          0.00000000e+00      
34              9.29278542e+00          0.00000000e+00      
Final           9.29278542e+00      
----------------------      

Algorithm: LevenbergMarquardt(
    trustregion = LevenbergMarquardtTrustRegion(
        β_uphill = 1.0
    ),
    descent = GeodesicAcceleration(
        descent = DampedNewtonDescent(
            initial_damping = 1.0,
            damping_fn = LevenbergMarquardtDampingFunction(
                increase_factor = 2.0,
                decrease_factor = 3.0,
                min_damping = 1.0e-8
            )
        ),
        finite_diff_step_geodesic = 0.1,
        α = 0.75
    ),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{true}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               1.16702595e+02          0.00000000e+00      
1               4.80497109e+01          3.19080865e+00      
2               2.15483384e+01          6.11610404e-01      
...     
112             9.29278542e+00          0.00000000e+00      
113             9.29278542e+00          1.96779581e-16      
Final           9.29278542e+00      
----------------------      
retcode: Stalled
u: 2-element Vector{Float64}:
 0.8489074606432829
 3.0226579109175553

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[f6369f11] ForwardDiff v0.10.38
  [2fda8390] LsqFit v0.15.0
  [8913a72c] NonlinearSolve v4.5.0
  [91a5bcdd] Plots v1.40.11
  [9a3f8284] Random v1.11.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

  [47edcb42] ADTypes v1.14.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [66dad0bd] AliasTables v1.1.3
  [4fba245c] ArrayInterface v7.18.0
  [4c555306] ArrayLayouts v1.11.1
  [d1d4a3ce] BitFlags v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [70df07ce] BracketingNonlinearSolve v1.1.2
  [2a0fbf3d] CPUSummary v0.2.6
  [d360d2e6] ChainRulesCore v1.25.1
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.29.0
  [3da002f7] ColorTypes v0.12.0
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.0
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
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  [187b0558] ConstructionBase v1.5.8
  [d38c429a] Contour v0.6.3
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.22
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.167.1
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.50
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  [ffbed154] DocStringExtensions v0.9.4
  [4e289a0a] EnumX v1.0.5
  [f151be2c] EnzymeCore v0.8.8
  [460bff9d] ExceptionUnwrapping v0.1.11
  [e2ba6199] ExprTools v0.1.10
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  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [a4df4552] FastPower v1.1.2
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  [6a86dc24] FiniteDiff v2.27.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
⌅ [f6369f11] ForwardDiff v0.10.38
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  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [28b8d3ca] GR v0.73.13
  [42e2da0e] Grisu v1.0.2
  [cd3eb016] HTTP v1.10.15
  [34004b35] HypergeometricFunctions v0.3.28
  [615f187c] IfElse v0.1.1
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.10
  [692b3bcd] JLLWrappers v1.7.0
  [682c06a0] JSON v0.21.4
  [ae98c720] Jieko v0.2.1
  [ba0b0d4f] Krylov v0.9.10
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.6
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.6.1
  [87fe0de2] LineSearch v0.1.4
  [7ed4a6bd] LinearSolve v3.7.2
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.1.0
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  [d41bc354] NLSolversBase v7.9.0
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  [8913a72c] NonlinearSolve v4.5.0
  [be0214bd] NonlinearSolveBase v1.5.1
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  [9a2c21bd] NonlinearSolveQuasiNewton v1.2.0
  [26075421] NonlinearSolveSpectralMethods v1.1.0
  [4d8831e6] OpenSSL v1.4.3
  [bac558e1] OrderedCollections v1.8.0
  [90014a1f] PDMats v0.11.33
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.3
  [91a5bcdd] Plots v1.40.11
  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [43287f4e] PtrArrays v1.3.0
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  [ae029012] Requires v1.3.1
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  [a2af1166] SortingAlgorithms v1.2.1
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  [276daf66] SpecialFunctions v2.5.0
  [860ef19b] StableRNGs v1.0.2
  [aedffcd0] Static v1.2.0
  [0d7ed370] StaticArrayInterface v1.8.0
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.4
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [2efcf032] SymbolicIndexingInterface v0.3.38
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [62fd8b95] TensorCore v0.1.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.28
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  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.22.0
  [45397f5d] UnitfulLatexify v1.6.4
  [41fe7b60] Unzip v0.2.0
  [6e34b625] Bzip2_jll v1.0.9+0
  [83423d85] Cairo_jll v1.18.4+0
  [ee1fde0b] Dbus_jll v1.14.10+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.6.5+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [a3f928ae] Fontconfig_jll v2.15.0+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.16+0
  [0656b61e] GLFW_jll v3.4.0+2
  [d2c73de3] GR_jll v0.73.13+0
  [78b55507] Gettext_jll v0.21.0+0
⌃ [7746bdde] Glib_jll v2.82.4+0
  [3b182d85] Graphite2_jll v1.3.14+1
  [2e76f6c2] HarfBuzz_jll v8.5.0+0
  [1d5cc7b8] IntelOpenMP_jll v2025.0.4+0
  [aacddb02] JpegTurbo_jll v3.1.1+0
  [c1c5ebd0] LAME_jll v3.100.2+0
  [88015f11] LERC_jll v4.0.1+0
  [1d63c593] LLVMOpenMP_jll v18.1.7+0
  [dd4b983a] LZO_jll v2.10.3+0
⌅ [e9f186c6] Libffi_jll v3.2.2+2
  [d4300ac3] Libgcrypt_jll v1.11.0+0
  [7e76a0d4] Libglvnd_jll v1.7.0+0
  [7add5ba3] Libgpg_error_jll v1.51.1+0
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.40.3+0
  [89763e89] Libtiff_jll v4.7.1+0
  [38a345b3] Libuuid_jll v2.40.3+0
  [856f044c] MKL_jll v2025.0.1+1
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.16+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.3.3+0
  [36c8627f] Pango_jll v1.56.1+0
  [30392449] Pixman_jll v0.44.2+0
⌅ [c0090381] Qt6Base_jll v6.7.1+1
⌅ [629bc702] Qt6Declarative_jll v6.7.1+2
⌅ [ce943373] Qt6ShaderTools_jll v6.7.1+1
⌃ [e99dba38] Qt6Wayland_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+2
  [2381bf8a] Wayland_protocols_jll v1.36.0+0
  [02c8fc9c] XML2_jll v2.13.6+1
  [aed1982a] XSLT_jll v1.1.42+0
  [ffd25f8a] XZ_jll v5.6.4+1
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+3
  [0c0b7dd1] Xorg_libXau_jll v1.0.12+0
  [935fb764] Xorg_libXcursor_jll v1.2.3+0
  [a3789734] Xorg_libXdmcp_jll v1.1.5+0
  [1082639a] Xorg_libXext_jll v1.3.6+3
  [d091e8ba] Xorg_libXfixes_jll v6.0.0+0
  [a51aa0fd] Xorg_libXi_jll v1.8.2+0
  [d1454406] Xorg_libXinerama_jll v1.1.5+0
  [ec84b674] Xorg_libXrandr_jll v1.5.4+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+1
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.2+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+3
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+1
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+1
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.1+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.9+0
  [214eeab7] fzf_jll v0.56.3+0
  [1a1c6b14] gperf_jll v3.1.1+1
  [a4ae2306] libaom_jll v3.11.0+0
  [0ac62f75] libass_jll v0.15.2+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.3+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.47+0
  [f27f6e37] libvorbis_jll v1.3.7+2
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2022.0.0+0
⌅ [1270edf5] x264_jll v2021.5.5+0
⌅ [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+2
  [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 v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+4
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [3f19e933] p7zip_jll v17.4.0+2

• Output of versioninfo()

Julia Version 1.11.4
Commit 8561cc3d68d (2025-03-10 11:36 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 12 × Apple M2 Max
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 10 default, 0 interactive, 5 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 10
  DYLD_FALLBACK_LIBRARY_PATH = /Users/hstrey/.julia/artifacts/c1600fa286afe4bf3616780a19b65285c63968ca/lib:/Users/hstrey/.julia/artifacts/b820a0a437e8501d06a17439abd84feaa5b6cca3/lib:/Users/hstrey/.julia/artifacts/5b90ad21b4b1af3a9446241fb5afe3e3b3eda941/lib:/Users/hstrey/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/lib/julia:/Users/hstrey/.julia/artifacts/c99c0e2b61a41b4b2294b30e9f7f26e50c2e38eb/lib:/Users/hstrey/.julia/artifacts/9410bad2635eda2239b4a72ba4316c4aa8f5b76e/lib:/Users/hstrey/.julia/artifacts/3b568c51fbf75bfe59ac69d26b176034fdd63ebb/lib:/Users/hstrey/.julia/artifacts/21209a2ac399ce693d73daf1aa8d670fbc84d70f/lib:/Users/hstrey/.julia/artifacts/c59059ef20910985e15a497e3f3f9f5a01df2645/lib:/Users/hstrey/.julia/artifacts/38c2ea0f23a62cc587d9939b8338d89cc961ea34/lib:/Users/hstrey/.julia/artifacts/365365262519d2f165f6ca9bdc0f104718889a88/lib:/Users/hstrey/.julia/artifacts/becfd6f89f1a272ace2375b067f1153515ca70b3/lib:/Users/hstrey/.julia/artifacts/1ed65d60dbf4c95b71bed5c28505e017ea1de760/lib:/Users/hstrey/.julia/artifacts/6ebc40d37ee48f23c8a0edb94c2f1a8622edba3a/lib:/Users/hstrey/.julia/artifacts/1994697285dfe8747ff7ec6927666edc88750202/lib:/Users/hstrey/.julia/artifacts/c5d5b7c7e77b04af2eabde40ebbf379932d8bfd7/lib:/Users/hstrey/.julia/artifacts/81e1d2f3a1459f121eaae539b9549e9e740a6c62/lib:/Users/hstrey/.julia/artifacts/a3e73ecf5d803bb3792a23f0382a2b5573383647/lib:/Users/hstrey/.julia/artifacts/67723a86975c82b43f01cda306999b382d3435f0/lib:/Users/hstrey/.julia/artifacts/115f3a18328d7b88e31c9e3f095aeb12eb381710/lib:/Users/hstrey/.julia/artifacts/ca2831bf6edc5088aec5b329ea98364951d6cad0/lib:/Users/hstrey/.julia/artifacts/477447566a69a531a7a3f8e0130cbfe460b37eec/lib:/Users/hstrey/.julia/artifacts/b58891667c46c467bd51be0e963c1ef1f0314934/lib:/Users/hstrey/.julia/artifacts/0db9c3f6cf936a0da49e2ba954ba3e10bed6ad72/lib:/Users/hstrey/.julia/artifacts/1a7e22e66b523d9cb884cf85c3ec065b5fb3e5c3/lib:/Users/hstrey/.julia/artifacts/638182c11b24bfb41187d67770f2bee17fb08c74/lib:/Users/hstrey/.julia/artifacts/83ff444c229f9dd64a13999123a4eb14e632d67a/lib:/Users/hstrey/.julia/artifacts/6095fcd268ea712c0f786f5ff1a45bf0eb7b005e/lib:/Users/hstrey/.julia/artifacts/7ead0a440ba045155db235bff6602a984f08a651/lib:/Users/hstrey/.julia/artifacts/9d8a957aa3387b17b8639251016c87710db1a175/lib:/Users/hstrey/.julia/artifacts/63d48e4aab8721470f588bdeb1e2b462ee3b6a68/lib:/Users/hstrey/.julia/artifacts/a6dd1ba35c9f4dcddf8199ec2ad4e413630f4e27/lib:/Users/hstrey/.julia/artifacts/8da603395acfbdbef8c5de3b7223aeb9276ecbdb/lib:/Users/hstrey/.julia/artifacts/932f282690a789f3744abcd83fb9f68ba7ed4c19/lib:/Users/hstrey/.julia/artifacts/4b3b2d79556cc3aef6e3d8a234649cc85b91bb87/lib:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtConcurrent.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtCore.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtDBus.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtGui.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtNetwork.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtOpenGL.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtPrintSupport.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtSql.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtTest.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtWidgets.framework/Versions/A:/Users/hstrey/.julia/artifacts/7f2122f84c49e5b75c5b4cbf46bbdeb3b0ffc5da/lib/QtXml.framework/Versions/A:/Users/hstrey/.julia/artifacts/9ada70096e6dad3b5cfcb8d97f9aeaef17b5a941/lib:/Users/hstrey/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/bin/../lib/julia:/Users/hstrey/.julia/juliaup/julia-1.11.4+0.aarch64.apple.darwin14/bin/../lib:

Additional context

Add any other context about the problem here.

[hstrey]

This issue is probably the same as: #459

Is there a setting that returns the best value, even though it stalled. Why are there cases when it stalled and still returns a value different from the initial value?

[ChrisRackauckas]

32              9.29278542e+00          0.00000000e+00      
33              9.32421225e+00          0.00000000e+00      
Final           9.32421225e+00      

it computes the right value, and then returns the wrong one.

[hstrey]

@ChrisRackauckas @avik-pal Is there a Solver setting, that returns the best value?

[ChrisRackauckas]

That's not the thing. As I pointed out, it's just a weird bug. Check the in-place interface, does it only happen out of place?

[hstrey]

function res!(dβ,β,(x,y))
    dβ =  line_fct(x,β) .- y
end

prob = NonlinearLeastSquaresProblem(res!, [1,3], p=(x,y_line_n))
sol = solve(prob; maxiters =1000, show_trace = Val(true))

gives

Algorithm: GaussNewton(
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               0.00000000e+00          0.00000000e+00      
┌ Warning: Potential Rank Deficient Matrix Detected. Attempting to solve using Pivoted QR Factorization.
└ @ NonlinearSolveBaseLinearSolveExt ~/.julia/packages/NonlinearSolveBase/xDyV6/ext/NonlinearSolveBaseLinearSolveExt.jl:33
1               0.00000000e+00          0.00000000e+00      
Final           0.00000000e+00      
----------------------      
retcode: Success
u: 2-element Vector{Float64}:
 1.0
 3.0

I even tried

prob = NonlinearLeastSquaresProblem(NonlinearFunction(res!, resid_prototype = zeros(length(x))), [1.0,3.0], p=(x,y_line_n))

same result

[ChrisRackauckas]

Your res! function is nothing

function res!(dβ,β,(x,y))
    dβ .=  line_fct(x,β) .- y
end

[hstrey]

Your res! function is nothing

function res!(dβ,β,(x,y))
dβ .= line_fct(x,β) .- y
end

Damn dots. My bad. Unfortunately, this did not change anything:

Algorithm: GaussNewton(
    descent = NewtonDescent(),
    autodiff = AutoForwardDiff(),
    vjp_autodiff = AutoFiniteDiff(
        fdtype = Val{:forward}(),
        fdjtype = Val{:forward}(),
        fdhtype = Val{:hcentral}(),
        dir = true
    ),
    jvp_autodiff = AutoForwardDiff(),
    concrete_jac = Val{false}()
)

----            -------------           -----------         
Iter            f(u) 2-norm             Step 2-norm         
----            -------------           -----------         
0               4.94313810e+00          0.00000000e+00      
1               4.23716567e+00          2.49781338e-01      
2               4.23716567e+00          6.52285960e-16      
...     
31              4.23716567e+00          5.20463418e-16      
32              4.23716567e+00          9.91714903e-16      
33              4.94313810e+00          4.67931662e-16      
Final           4.94313810e+00      
----------------------

retcode: Stalled
u: 2-element Vector{Float64}:
 1.0
 3.0