OptimizationLBFGSB.LBFGSB() produces wrong results with retcode: Success

**Describe the bug 🐞**

Hi everyone. I've run into this runtime error that worries me a bit. I was minimizing a typical chi squared function using `OptimizationLBFGSB.LBFGSB()`. The optimization returns success but the result is wrong.

I've discovered this behaviour with the last 4.x version of `Optimization.jl` using `Optimization.LBFGS()`, but here I provide a MWE for version 5.1.0 that reproduces the bug.

<img width="720" height="540" alt="Image" src="https://github.com/user-attachments/assets/890a9f0f-43dd-4dc2-9c8a-2eeae20ce043" />

As you can see on the image, the minimum is around `-0.05`, but when I call the method `LBFGSB()` from `OptimizationLBFGSB` package,
 ```julia
sol = solve(prob, OptimizationLBFGSB.LBFGSB())
 ```

I get
```julia
retcode: Success
u: 1-element Vector{Float64}:
 0.0
```

which is a success retcode with a minimum around `0.0`. Looking at the figure, that's obviously wrong. There are no warnings whatsoever.

If I use `Optim`'s  `LBFGS()` method instead, everything works:
```julia
sol = solve(prob, Optim.LBFGS())
```

returns
```julia
retcode: Success
u: 1-element Vector{Float64}:
 -0.051422488572892285
```

which is the correct value.

**Expected behavior**

I should be able to call `OptimizationLBFGSB.LBFGSB()` and get a minimum around `-0.05` with a `retcode: Success`.

**Minimal Reproducible Example 👇**

I've pregenerated the data for ease of use. The function I'm minimizing is a Poissonian likelyhood function with some nuisance parameters (the ones to be minimized over). 

```julia
using Optimization, OptimizationOptimJL, OptimizationLBFGSB, ForwardDiff, CairoMakie

"Experimental number of events."
const ne = [47.79016955366216, 54.63792672045489, 60.6817081483305, 65.85497617511764,
70.10163120593351, 73.38214524249031, 75.6679992088981, 76.9449555834446, 77.20918553594912,
76.46915655141063, 74.74232402982297, 72.05645354279015, 68.44666004402201, 63.956275455187374,
58.63429503572871, 52.53457348342481, 45.677188154035534, 38.7314886941981, 34.19260165003558,
30.784750516477747, 27.387995197108484, 24.00145774130718, 20.687966069161696, 17.637911910103306,
14.93245414792653, 12.4489653347761, 10.181537719538321, 8.148303027435635, 6.361941181550973,
4.829627414524656, 3.552527822049159, 2.5264917405123013, 1.7421104640301057, 1.1877485347281902,
0.8467200821260764, 0.6560958454993128]

"Theoretical number of events."
const nt = [49.00928880337846, 56.09394530248748, 62.37909255858915, 67.79690028474204,
72.28975301404762, 75.8162261685694, 78.3457614258788, 79.86188067534194, 80.35848905789322,
79.84174847321458, 78.32689914964128, 75.83959322777797, 72.41302839568749, 68.0888342687985,
62.914584567966486, 56.941011087706656, 50.01050515306522, 41.89887406295331, 36.503137537870884,
32.96797889924509, 29.466821579372933, 25.959186733715818, 22.509873814723917, 19.311591400637997,
16.448043988519792, 13.799326941778979, 11.362380032036715, 9.158257568882474, 7.202570686822948,
5.505387789445479, 4.070660173093367, 2.8968757912937115, 1.9770626122012342, 1.3024644039013222,
0.8738309918479059, 0.6573023347540636]

function chi2(alpha, n_exp, n_th)
    total_chi = 0.0
    # Add nuisance parameters
    n_th = (1 + alpha[1]) * n_th

    total_chi = 0.0
    for i in eachindex(n_exp)
        if n_exp[i] == 0.0
            total_chi += 2 * n_th[i]
        else
            total_chi += 2 * (n_th[i] - n_exp[i] + n_exp[i] * log(n_exp[i] / n_th[i]))
        end
    end

    return total_chi
end


function main()
    f(u, p) = chi2(u, ne, nt)

    u0 = [0.0,]
    lb = [-1.0,]
    ub = [1.0,]

    optf = OptimizationFunction(f, AutoForwardDiff())
    prob = OptimizationProblem(optf, u0; lb = lb, ub = ub)
    sol = solve(prob, OptimizationLBFGSB.LBFGSB())

    return sol
end

# Returns retcode: Success with minimum at 0.0, wrong result
sol = main()
sol.objective
```

Next we call our main function with `Optim.LBFGS()`:

```julia
function main2()
    f(u, p) = chi2(u, ne, nt)

    u0 = [0.0,]
    lb = [-1.0,]
    ub = [1.0,]

    optf = OptimizationFunction(f, AutoForwardDiff())
    prob = OptimizationProblem(optf, u0; lb = lb, ub = ub)
    sol = solve(prob, Optim.LBFGS())

    return sol
end

# Returns retcode: Success with minimum at around -0.05, correct result
sol2 = main2()
sol2.objective
```

**Error & Stacktrace ⚠️**

There is no error nor stacktrace, but a runtime error.

**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia
Status `~/mwe/Project.toml`
  [13f3f980] CairoMakie v0.15.6
  [f6369f11] ForwardDiff v1.3.0
  [7f7a1694] Optimization v5.1.0
  [22f7324a] OptimizationLBFGSB v1.2.1
  [36348300] OptimizationOptimJL v0.4.8
```

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

```julia
Status `~/mwe/Manifest.toml`
  [47edcb42] ADTypes v1.19.0
  [621f4979] AbstractFFTs v1.5.0
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.4.0
  [35492f91] AdaptivePredicates v1.2.0
  [66dad0bd] AliasTables v1.1.3
  [27a7e980] Animations v0.4.2
  [4fba245c] ArrayInterface v7.22.0
  [67c07d97] Automa v1.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.8
  [18cc8868] BaseDirs v1.3.2
  [fa961155] CEnum v0.5.0
  [96374032] CRlibm v1.0.2
  [159f3aea] Cairo v1.1.1
  [13f3f980] CairoMakie v0.15.6
  [d360d2e6] ChainRulesCore v1.26.0
  [a2cac450] ColorBrewer v0.4.2
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [a33af91c] CompositionsBase v0.1.2
  [95dc2771] ComputePipeline v0.1.4
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.19.3
  [e2d170a0] DataValueInterfaces v1.0.0
  [927a84f5] DelaunayTriangulation v1.6.5
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.7.12
  [31c24e10] Distributions v0.25.122
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.5
  [429591f6] ExactPredicates v2.2.9
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [411431e0] Extents v0.1.6
  [7a1cc6ca] FFTW v1.10.0
  [9aa1b823] FastClosures v0.3.2
  [5789e2e9] FileIO v1.17.1
⌅ [8fc22ac5] FilePaths v0.8.3
  [48062228] FilePathsBase v0.9.24
  [1a297f60] FillArrays v1.15.0
  [6a86dc24] FiniteDiff v2.29.0
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v1.3.0
  [b38be410] FreeType v4.1.1
  [663a7486] FreeTypeAbstraction v0.10.8
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.2.0
  [5c1252a2] GeometryBasics v0.5.10
  [a2bd30eb] Graphics v1.1.3
  [3955a311] GridLayoutBase v0.11.2
  [42e2da0e] Grisu v1.0.2
  [34004b35] HypergeometricFunctions v0.3.28
  [2803e5a7] ImageAxes v0.6.12
  [c817782e] ImageBase v0.1.7
  [a09fc81d] ImageCore v0.10.5
  [82e4d734] ImageIO v0.6.9
  [bc367c6b] ImageMetadata v0.9.10
  [9b13fd28] IndirectArrays v1.0.0
  [d25df0c9] Inflate v0.1.5
  [a98d9a8b] Interpolations v0.16.2
  [d1acc4aa] IntervalArithmetic v1.0.2
  [8197267c] IntervalSets v0.7.12
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [f1662d9f] Isoband v0.1.1
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.1
  [682c06a0] JSON v1.3.0
  [ae98c720] Jieko v0.2.1
  [b835a17e] JpegTurbo v0.1.6
  [5ab0869b] KernelDensity v0.6.10
  [5be7bae1] LBFGSB v0.4.1
  [b964fa9f] LaTeXStrings v1.4.0
  [8cdb02fc] LazyModules v0.3.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.1
  [d3d80556] LineSearches v7.4.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
  [ee78f7c6] Makie v0.24.6
  [dbb5928d] MappedArrays v0.4.2
  [0a4f8689] MathTeXEngine v0.6.7
  [e1d29d7a] Missings v1.2.0
  [e94cdb99] MosaicViews v0.3.4
  [2e0e35c7] Moshi v0.3.7
  [d41bc354] NLSolversBase v7.10.0
  [77ba4419] NaNMath v1.1.3
  [f09324ee] Netpbm v1.1.1
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.17.0
  [52e1d378] OpenEXR v0.3.3
  [429524aa] Optim v1.13.2
  [7f7a1694] Optimization v5.1.0
  [bca83a33] OptimizationBase v4.0.2
  [22f7324a] OptimizationLBFGSB v1.2.1
  [36348300] OptimizationOptimJL v0.4.8
  [bac558e1] OrderedCollections v1.8.1
  [90014a1f] PDMats v0.11.36
  [f57f5aa1] PNGFiles v0.4.4
  [19eb6ba3] Packing v0.5.1
  [5432bcbf] PaddedViews v0.5.12
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.3
  [eebad327] PkgVersion v0.3.3
  [995b91a9] PlotUtils v1.4.4
  [647866c9] PolygonOps v0.1.2
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.34
  [aea7be01] PrecompileTools v1.3.3
  [21216c6a] Preferences v1.5.0
  [33c8b6b6] ProgressLogging v0.1.5
  [92933f4c] ProgressMeter v1.11.0
  [43287f4e] PtrArrays v1.3.0
  [4b34888f] QOI v1.0.1
  [1fd47b50] QuadGK v2.11.2
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.39.0
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [79098fc4] Rmath v0.9.0
  [5eaf0fd0] RoundingEmulator v0.2.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.16
  [fdea26ae] SIMD v3.7.2
  [0bca4576] SciMLBase v2.127.0
  [a6db7da4] SciMLLogging v1.5.0
  [c0aeaf25] SciMLOperators v1.11.0
  [431bcebd] SciMLPublic v1.0.0
  [53ae85a6] SciMLStructures v1.7.0
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [65257c39] ShaderAbstractions v0.5.0
  [992d4aef] Showoff v1.0.3
  [73760f76] SignedDistanceFields v0.4.0
  [699a6c99] SimpleTraits v0.9.5
  [45858cf5] Sixel v0.1.5
  [a2af1166] SortingAlgorithms v1.2.2
  [9f842d2f] SparseConnectivityTracer v1.1.3
  [0a514795] SparseMatrixColorings v0.4.23
  [276daf66] SpecialFunctions v2.6.1
  [860ef19b] StableRNGs v1.0.4
  [cae243ae] StackViews v0.1.2
  [90137ffa] StaticArrays v1.9.15
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.1
  [2913bbd2] StatsBase v0.34.8
  [4c63d2b9] StatsFuns v1.5.2
  [09ab397b] StructArrays v0.7.2
  [ec057cc2] StructUtils v2.6.0
  [2efcf032] SymbolicIndexingInterface v0.3.46
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
  [5d786b92] TerminalLoggers v0.1.7
  [731e570b] TiffImages v0.11.6
  [3bb67fe8] TranscodingStreams v0.11.3
  [981d1d27] TriplotBase v0.1.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.25.1
  [e3aaa7dc] WebP v0.1.3
  [efce3f68] WoodburyMatrices v1.0.0
  [6e34b625] Bzip2_jll v1.0.9+0
  [4e9b3aee] CRlibm_jll v1.0.1+0
  [83423d85] Cairo_jll v1.18.5+0
  [5ae413db] EarCut_jll v2.2.4+0
  [2e619515] Expat_jll v2.7.3+0
⌅ [b22a6f82] FFMPEG_jll v6.1.3+0
  [f5851436] FFTW_jll v3.3.11+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.13.4+0
  [559328eb] FriBidi_jll v1.0.17+0
  [b0724c58] GettextRuntime_jll v0.22.4+0
  [59f7168a] Giflib_jll v5.2.3+0
  [7746bdde] Glib_jll v2.86.0+0
  [3b182d85] Graphite2_jll v1.3.15+0
  [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [905a6f67] Imath_jll v3.1.11+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.1.3+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.0.1+0
  [1d63c593] LLVMOpenMP_jll v18.1.8+0
  [dd4b983a] LZO_jll v2.10.3+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
  [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.41.2+0
  [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.41.2+0
  [856f044c] MKL_jll v2025.2.0+0
  [e7412a2a] Ogg_jll v1.3.6+0
  [6cdc7f73] OpenBLASConsistentFPCSR_jll v0.3.29+0
  [18a262bb] OpenEXR_jll v3.2.4+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.5.2+0
  [36c8627f] Pango_jll v1.57.0+0
⌅ [30392449] Pixman_jll v0.44.2+0
  [f50d1b31] Rmath_jll v0.5.1+0
  [ffd25f8a] XZ_jll v5.8.1+0
  [4f6342f7] Xorg_libX11_jll v1.8.12+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.7+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [9a68df92] isoband_jll v0.2.3+0
  [a4ae2306] libaom_jll v3.13.1+0
  [0ac62f75] libass_jll v0.17.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [b53b4c65] libpng_jll v1.6.50+0
  [075b6546] libsixel_jll v1.10.5+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [c5f90fcd] libwebp_jll v1.6.0+0
  [1317d2d5] oneTBB_jll v2022.0.0+1
  [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [8bf52ea8] CRC32c 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
  [ac6e5ff7] JuliaSyntaxHighlighting v1.12.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.12.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.3.0
  [44cfe95a] Pkg v1.12.0
  [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
  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.12.0
  [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 v1.3.0+1
  [deac9b47] LibCURL_jll v8.11.1+1
  [e37daf67] LibGit2_jll v1.9.0+0
  [29816b5a] LibSSH2_jll v1.11.3+1
  [14a3606d] MozillaCACerts_jll v2025.5.20
  [4536629a] OpenBLAS_jll v0.3.29+0
  [05823500] OpenLibm_jll v0.8.7+0
  [458c3c95] OpenSSL_jll v3.5.1+0
  [efcefdf7] PCRE2_jll v10.44.0+1
  [bea87d4a] SuiteSparse_jll v7.8.3+2
  [83775a58] Zlib_jll v1.3.1+2
  [8e850b90] libblastrampoline_jll v5.13.1+1
  [8e850ede] nghttp2_jll v1.64.0+1
  [3f19e933] p7zip_jll v17.5.0+2
Info Packages marked with ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`
```

  - Output of `versioninfo()`

```julia
Julia Version 1.12.0
Commit b907bd0600f (2025-10-07 15:42 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 20 × 12th Gen Intel(R) Core(TM) i7-12700H
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, alderlake)
  GC: Built with stock GC
Threads: 1 default, 1 interactive, 1 GC (on 20 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_VSCODE_REPL = 1
```

**Additional context**

I've tried a derivative-free method like `Optim.NelderMead()` and get the correct result, too.


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OptimizationLBFGSB.LBFGSB() produces wrong results with retcode: Success #1094

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OptimizationLBFGSB.LBFGSB() produces wrong results with retcode: Success #1094

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