Key error when adding a complementarity condition

Specific Domains Optimization (Mathematical)
1

I’m working to translate some economics models from GAMS into Julia using the Complementarity package and I’m running into an issue where a variable is defined on a larger set than its complementary equation. Here is a small example of the situation:

model = MCPModel()
A = [1,2,3,4]
B = [1,2,3]
@variable(model, X[A])
@mapping(model, Y[x = B], x^2)
@complementarity(model, Y, X)

Where B is a proper subset of A. Running this I get a KeyError because A contains elements that B does not.

KeyError: key 4 not found

1. <mark>**getindex**</mark>@*dict.jl:498* [inlined]
2. <mark>**getindex**</mark>@*DenseAxisArray.jl:51* [inlined]
3. <mark>**_getindex_recurse**</mark>@*DenseAxisArray.jl:309* [inlined]
4. <mark>**to_index**</mark>@*DenseAxisArray.jl:318* [inlined]
5. <mark>**getindex**(::JuMP.Containers.DenseAxisArray{JuMP.NonlinearExpression, 1, Tuple{Vector{Int64}}, Tuple{JuMP.Containers._AxisLookup{Dict{Int64, Int64}}}}, ::Int64)</mark>@*DenseAxisArray.jl:325*
6. <mark>**macro expansion**</mark>@*mcp.jl:435* [inlined]
7. <mark>**top-level scope**</mark>@*[Local: 7](http://localhost:1234/edit?id=7fb5cec0-3d9b-11ed-0a5a-91cf86764404#)* [inlined]

My question is: Is there a workaround for this or should I submit report to the complementarity package authors?

GAMS solves this by associating any keys not found to 0.

2

The error message could be better, but the workatound is to not have mismatched keys?

3

The error message is quite clear, there are extra keys in the variable that aren’t in the equation. The workaround can’t be to “not have mismatched keys” because I’m implementing a model where the mapping is only defined on a subset of the variable domain.

My temporary solution to is to implement a kronecker-delta function that “turns-off” the keys that aren’t needed. I’m not crazy about this; however, since it requires a special function for each mapping.

1 Like
4

You should open an issue with a feature request at GitHub - chkwon/Complementarity.jl: provides a modeling interface for mixed complementarity problems (MCP) and math programs with equilibrium problems (MPEC) via JuMP.

I don’t know if @chkwon is actively maintaining Complementarity.jl, but I’ll review a pull request if you want to dig into the details and make one.

1 Like
5

Thanks, I’ll start digging through to see if I can get things working.

Thanks again for the suggestions.

6

I think the best solution is a macro for the Kronecker-Delta function, define the mapping on the entire set, and put the filter condition in X kron_δ.

Something like:

macro kron_δ(x,X)
	x = esc(x)
	X = esc(X)
	quote
		$x in $X
	end
end

model = MCPModel()
A = [1,2,3,4]
B = [1,2,3]

@variable(model, X[A])
@mapping(model, Y[x = A], @δ(x,B)*X[x]^x)
@complementarity(model, Y, X)

I’m new to Julia, so this may not be the “best” method, but the macro seems to be the key.

Thanks again!

7

I am maintaining Complementarity.jl in a minimal way :slight_smile:

But I think the feature Mitch raised is very useful. I just saw a PR. Thanks!

1 Like