`mul!(::Matrix, ::ArrayPartition, ::Adjoint(ArrayPartition))`

Start by running the MWE and comparing the working u * v' call with mul!(H, u, v'). Inspect src/array_partition.jl around line 151 and the LinearAlgebra transpose stack trace, especially the two-dimensional indexing and bounds check. Done means the in-place multiplication completes without the reported BoundsError for the shown ArrayPartition values.

https://github.com/JuliaNLSolvers/Optim.jl/pull/972

MWE

using RecursiveArrayTools, LinearAlgebra
u = ArrayPartition(rand(2), rand(1))
v = copy(u)
H = u * v' # works
mul!(H, u, v') # error

julia> mul!(H,u,v')                                                                         
ERROR: BoundsError: attempt to access Tuple{Vector{Float64}, Vector{Float64}} at index [3]                 
Stacktrace:                                                                                 
 [1] getindex                                                                                                                                                                          
   @ ~/.julia/dev/RecursiveArrayTools.jl/src/array_partition.jl:151 [inlined]                                                                                                                                        
 [2] copy_transpose!(B::Matrix{Float64}, ir_dest::UnitRange{Int64}, jr_dest::UnitRange{Int64}, A::ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}, ir_src::UnitRange{Int64}, jr_src::UnitRange{Int64})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/transpose.jl:197                                                       
 [3] copy_transpose!                                                                                                                 
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:693 [inlined]                                                            
 [4] _generic_matmatmul!(C::Matrix{Float64}, tA::Char, tB::Char, A::ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}, B::ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}, _add::LinearAlgebra.MulAddMul{true, 
true, Bool, Bool})                                                                                                                   
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:834                                                          
 [5] generic_matmatmul!                                                                                                              
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:801 [inlined]                                                              
 [6] mul!                                                                                                                            
   @ /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:478 [inlined]                                                            
 [7] mul!(C::Matrix{Float64}, A::ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}, B::Adjoint{Float64, ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}})
   @ LinearAlgebra /Applications/Julia-1.7.app/Contents/Resources/julia/share/julia/stdlib/v1.7/LinearAlgebra/src/matmul.jl:275
 [8] top-level scope                                                              
   @ REPL[134]:1                         

in LinearAlgebra/transpose.jl, v is being treated as an AbstractVecOrMat and is being accessed as follows v[3,1]

julia> checkbounds(Bool,v,3,1)
true

julia> v[3,1]
ERROR: BoundsError: attempt to access Tuple{Vector{Float64}, Vector{Float64}} at index [3]
Stacktrace:
 [1] getindex(A::ArrayPartition{Float64, Tuple{Vector{Float64}, Vector{Float64}}}, i::Int64, j::Int64)
   @ RecursiveArrayTools ~/.julia/dev/RecursiveArrayTools.jl/src/array_partition.jl:151