WIP: add a replacement for Symbolics.jl

[odow]

x-ref jump-dev/MathOptInterface.jl#2533

[ccoffrin]

Can we also update the package deps in this PR?

[odow]

I did in #38. I'll tag a release

[ccoffrin]

Is this still required? https://github.com/lanl-ansi/MathOptSymbolicAD.jl/blob/od/symbolic/Project.toml#L14

[odow]

Hopefully by the time I finish this PR, no. It's still a WIP

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[odow]

import MathOptInterface as MOI
import MathOptSymbolicAD

function _expr_to_symbolics(expr::MathOptSymbolicAD._Node)
    if expr.head == MathOptSymbolicAD._OP_COEFFICIENT
        return MOI.VariableIndex(-expr.index)
    elseif expr.head == MathOptSymbolicAD._OP_VARIABLE
        return MOI.VariableIndex(expr.index)
    elseif expr.head == MathOptSymbolicAD._OP_OPERATION
        return MOI.ScalarNonlinearFunction(
            expr.operation,
            Any[_expr_to_symbolics(c) for c in expr.children],
        )
    else
        @assert expr.head == MathOptSymbolicAD._OP_INTEGER_EXPONENT
        return MOI.ScalarNonlinearFunction(
            :^,
            Any[_expr_to_symbolics(expr.children[1]), expr.index],
        )
    end
end

x = MOI.VariableIndex.(1:4)
model = MOI.Nonlinear.Model()
for i in 1:3
    MOI.Nonlinear.add_constraint(model, :($(x[4]) * log($(x[i]) + $i)), MOI.LessThan(2.0))
end

variable_order = Dict(xi.value => i for (i, xi) in enumerate(x))
functions = map(values(model.constraints)) do c
    expr = MathOptSymbolicAD._to_expr(model, c.expression, variable_order, Any[])
    return MathOptSymbolicAD._Function(model, expr)
end

f = first(functions)
g = _expr_to_symbolics(f.expr)
x, ∇f, H, ∇²f = MathOptSymbolicAD.gradient_and_hessian(x -> x.value > 0, g)

julia> x
2-element Vector{MathOptInterface.VariableIndex}:
 MOI.VariableIndex(1)
 MOI.VariableIndex(2)

julia> ∇f
2-element Vector{Any}:
 log(+(MOI.VariableIndex(2), MOI.VariableIndex(-1)))
 *(MOI.VariableIndex(1), /((1), +(MOI.VariableIndex(2), MOI.VariableIndex(-1))))

julia> H
2-element Vector{Tuple{Int64, Int64}}:
 (1, 2)
 (2, 2)

julia> ∇²f
2-element Vector{Any}:
 /((1), +(MOI.VariableIndex(2), MOI.VariableIndex(-1)))
 *(MOI.VariableIndex(1), /((-1), ^(+(MOI.VariableIndex(2), MOI.VariableIndex(-1)), (2))))