feat: add structural_simplify for optimization systems

Author: AayushSabharwal

src/systems/systems.jl

@@ -57,6 +57,9 @@ function __structural_simplify(
     if has_noise_eqs(sys) && get_noise_eqs(sys) !== nothing
         throw(ArgumentError("Cannot simplify systems with `noise_eqs`"))
     end
+    if isempty(equations(sys)) && !is_time_dependent(sys) && !_iszero(cost(sys))
+        return simplify_optimization_system(sys; kwargs..., sort_eqs, simplify)
+    end
 
     sys = expand_connections(sys)
     state = TearingState(sys; sort_eqs)
@@ -148,6 +151,36 @@ function __structural_simplify(
     end
 end
 
+function simplify_optimization_system(sys::System; split = true, kwargs...)
+    sys = flatten(sys)
+    cons = constraints(sys)
+    econs = Equation[]
+    icons = similar(cons, 0)
+    for e in cons
+        if e isa Equation
+            push!(econs, e)
+        else
+            push!(icons, e)
+        end
+    end
+    nlsys = System(econs, unknowns(sys), parameters(sys); name = :___tmp_nlsystem)
+    snlsys = structural_simplify(nlsys; fully_determined = nothing, kwargs...)
+    obs = observed(snlsys)
+    subs = Dict(eq.lhs => eq.rhs for eq in observed(snlsys))
+    seqs = equations(snlsys)
+    cons_simplified = similar(cons, length(icons) + length(seqs))
+    for (i, eq) in enumerate(Iterators.flatten((seqs, icons)))
+        cons_simplified[i] = fixpoint_sub(eq, subs)
+    end
+    newsts = setdiff(unknowns(sys), keys(subs))
+    @set! sys.constraints = cons_simplified
+    @set! sys.observed = [observed(sys); obs]
+    newcost = fixpoint_sub.(get_costs(sys), (subs,))
+    @set! sys.costs = newcost
+    @set! sys.unknowns = newsts
+    return sys
+end
+
 function __num_isdiag_noise(mat)
     for i in axes(mat, 1)
         nnz = 0