Hi all,

I’m trying to formulate a nonlinear optimization problem with JuMP. Specifically, I’m looking to minimize the sum of the products of certain values in a matrix where one matrix is variable, and two additional matrices are constants. My question is how should I be handling an optimization problem where my variables are a 2D or 3D matrix of floats.

The objective function can be expressed as:

min \sum_{i=1}^n \alpha_i \prod_{s=1}^S exp(-w_{i,s}*x_{i,s})

I’ve run in to a number of problems trying to formulate this properly, since JuMP has restrictions on handling arrays in user defined functions, but here is my latest attempt:

```
using JuMP, Ipopt
function main(row, col)
w = rand(row, col)
α = rand(row)
m = Model(solver = IpoptSolver())
@variable(m, x[1:row*col] >= 0)
function myf(a...)
running_sum = 0
for i in length(α)
sub_product = 1
for s in col
sub_product *= exp(-w[i, s] * a[i + (s-1)*row])
end
running_sum += α[i] * sub_product
end
return running_sum
end
JuMP.register(m, :myf, row*col, myf, autodiff=true)
obj_expr = Expr(:call, :myf, [x[i] for i=1:row*col]...)
@NLobjective(m, :Min, obj_expr)
solve(m)
return m
end
println(main(4,2))
```

Which gives the error:

```
ERROR: LoadError: MethodError: no method matching parseNLExpr_runtime(::JuMP.Model, ::Expr, ::Array{ReverseDiffSparse.NodeData,1}, ::Int64, ::Array{Float64,1})
Closest candidates are:
parseNLExpr_runtime(::JuMP.Model, !Matched::Number, ::Any, ::Any, ::Any) at /Users/u/.julia/v0.6/JuMP/src/parsenlp.jl:196
parseNLExpr_runtime(::JuMP.Model, !Matched::JuMP.Variable, ::Any, ::Any, ::Any) at /Users/u/.julia/v0.6/JuMP/src/parsenlp.jl:202
parseNLExpr_runtime(::JuMP.Model, !Matched::JuMP.NonlinearExpression, ::Any, ::Any, ::Any) at /Users/u/.julia/v0.6/JuMP/src/parsenlp.jl:208
...
Stacktrace:
[1] macro expansion at /Users/u/.julia/v0.6/JuMP/src/parsenlp.jl:226 [inlined]
[2] macro expansion at /Users/u/.julia/v0.6/JuMP/src/macros.jl:1157 [inlined]
[3] main(::Int64, ::Int64) at /Users/u/Documents/test2.jl:26
[4] include_from_node1(::String) at ./loading.jl:576 [5] include(::String) at ./sysimg.jl:14
[6] process_options(::Base.JLOptions) at ./client.jl:305
[7] _start() at ./client.jl:371
while loading /Users/u/Documents/test2.jl, in expression starting on line 31
```

I believe my error is in how I define and pass the x variables, but I’m not quite sure why. I initially tried to represent x using `x[1:row, 1:col]`

, but seeing as the splatting `...`

syntax reduces a multi-dimensional array to a single dimension, I just defined it here as 1D. I have the freedom to reformat the inputs like this, but in practice the dimensions will be much larger than 4x2, probably on the order of 100x100.

I’m new to JuMP and Julia, so I’d appreciate any suggestions on how to better format this problem, especially since I plan incorporate additional constants, meaning that x will soon represent a 3-dimensional matrix (where it is currently 2-dimensional).