Rename local initialize_subproblem → initialize_subsolve

Sync the apply-PR's local `NestedAlgorithm` definition with the rename
landing in #115. Once #115 merges, this local definition will be
removed entirely in favor of `AIE.NestedAlgorithm`.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

Author: mtfishman

src/apply/apply_operators.jl

@@ -13,10 +13,10 @@ using NamedGraphs.GraphsExtensions: all_edges, boundary_edges
 
 abstract type NestedAlgorithm <: AI.Algorithm end
 
-function initialize_subproblem(
+function initialize_subsolve(
         problem::AI.Problem, algorithm::AI.Algorithm, state::AI.State
     )
-    return throw(MethodError(initialize_subproblem, (problem, algorithm, state)))
+    return throw(MethodError(initialize_subsolve, (problem, algorithm, state)))
 end
 
 function finalize_substate!(
@@ -27,7 +27,7 @@ function finalize_substate!(
 end
 
 function AI.step!(problem::AI.Problem, algorithm::NestedAlgorithm, state::AI.State)
-    subproblem, subalgorithm, substate = initialize_subproblem(problem, algorithm, state)
+    subproblem, subalgorithm, substate = initialize_subsolve(problem, algorithm, state)
     AI.solve!(subproblem, subalgorithm, substate)
     finalize_substate!(problem, algorithm, state, substate)
     return state
@@ -89,7 +89,7 @@ function AI.initialize_state!(
     return state
 end
 
-function initialize_subproblem(
+function initialize_subsolve(
         problem::ApplyOperatorsProblem, algorithm::ApplyOperators,
         state::ApplyOperatorsState
     )