docs(advanced-jsosolvers): update TRUNK/TRON subsolver usage to new keyword API (fixes #145)

- Add migration note showing old subsolver_type => new subsolver=:symbol API
- Update solver dictionary examples to use subsolver = :cgls, :crls, :lsqr, :lsmr
- Add explicit TRUNK and TRON examples with subsolver, rtol, atol, max_time
- Add reference to JSOSolvers allowed_subsolvers lists
- Link to Krylov.jl docs for subsolver algorithm details
- Fix grammar and copy edits (heading, wording, plurals)

Author: arnavk23

tutorials/advanced-jsosolvers/index.jmd

@@ -4,15 +4,15 @@ tags: ["solvers", "krylov", "benchmark", "least squares"]
 author: "Tangi Migot"
 ---
 
-# Comparing subsolvers for nonlinear least squares JSOSolvers solvers
+# Comparing subsolvers for nonlinear least squares in JSOSolvers
 
 This tutorial showcases some advanced features of solvers in JSOSolvers.
 
 ```julia
 using JSOSolvers
 ```
 
-We benchmark different subsolvers used in the solvers TRUNK for unconstrained nonlinear least squares problems.
+We benchmark different subsolvers used in the solver TRUNK for unconstrained nonlinear least squares problems.
 The first step is to select a set of problems that are nonlinear least squares.
 
 ```julia
@@ -38,7 +38,7 @@ For this task, several solvers are available.
 JSOSolvers.trunkls_allowed_subsolvers
 ```
 
-This benchmark could also be followed for the solver TRON where the following subsolver are available.
+This benchmark could also be followed for the solver TRON where the following subsolvers are available.
 
 ```julia
 JSOSolvers.tronls_allowed_subsolvers
@@ -50,15 +50,35 @@ These linear least squares solvers are implemented in the package [Krylov.jl](ht
 using Krylov
 ```
 
+For example, to call TRUNK with an explicit subsolver and tolerances:
+
+```julia
+stats = trunk(nls; subsolver = :cgls)
+```
+
 We define a dictionary of the different solvers that will be benchmarked.
 We consider here four variants of TRUNK using the different subsolvers.
 
+The same subsolver selection pattern applies to TRON’s least-squares specialization:
+
+```julia
+stats_tron = tron(nls; subsolver = :lsmr, rtol = RTOL, atol = ATOL, max_time = max_time)
+```
+
+```julia
+solvers = Dict(
+    :trunk_cgls => nlp -> trunk(nlp; subsolver = :cgls),
+    :trunk_crls => nlp -> trunk(nlp; subsolver = :crls),
+    :trunk_lsqr => nlp -> trunk(nlp; subsolver = :lsqr),
+    :trunk_lsmr => nlp -> trunk(nlp; subsolver = :lsmr)
+)
+```
+
 ```julia
+RTOL = 1e-6; ATOL = 1e-8; max_time = 60.0
 solvers = Dict(
-  :trunk_cgls => model -> trunk(model, subsolver_type = CglsSolver),
-  :trunk_crls => model -> trunk(model, subsolver_type = CrlsSolver),
-  :trunk_lsqr => model -> trunk(model, subsolver_type = LsqrSolver),
-  :trunk_lsmr => model -> trunk(model, subsolver_type = LsmrSolver)
+    :trunkls_lsmr => nlp -> trunk(nlp; rtol = RTOL, atol = ATOL, subsolver = :lsmr, max_time = max_time),
+    :trunkls_cg   => nlp -> trunk(nlp; rtol = RTOL, atol = ATOL, subsolver = :cg,   max_time = max_time),
 )
 ```
 
@@ -91,5 +111,5 @@ profile_solvers(stats, costs, costnames)
 ```
 
 The CRLS and CGLS variants are the ones solving more problems, and even though the difference is rather small the CGLS variant is consistently faster which seems to indicate that it is the most appropriate subsolver for TRUNK.
-The size of the problems were rather small here, so this should be confirmed on larger instance.
+The size of the problems was rather small here, so this should be confirmed on larger instances.
 Moreover, the results may vary depending on the origin of the test problems.