Should the `state` be updated in `solver_step!` or `solve!` directly?

[benedict-96]

The NonlinearSolverStatus was made immutable in #109.

With commit 85d665a we now have:

SimpleSolvers.jl/src/optimization/optimizer.jl

Lines 182 to 197 in 85d665a

	function solve!(x::AbstractVector, state::OptimizerState, opt::Optimizer)
	initialize_state!(state)
	while true
	increase_iteration_number!(state)
	solver_step!(x, state, opt)
	status = OptimizerStatus(state, cache(opt), value(problem(opt), x); config = config(opt))
	meets_stopping_criteria(status, opt, state) && break
	update!(state, gradient(opt), x)
	end
	warn_iteration_number(state, config(opt))
	status = OptimizerStatus(state, cache(opt), value(problem(opt), x); config = config(opt))
	OptimizerResult(status, x, value(problem(opt), x))
	end

for the optimizer and

SimpleSolvers.jl/src/nonlinear/nonlinear_solver.jl

Lines 144 to 159 in 85d665a

	function solve!(x::AbstractArray, s::NonlinearSolver, state::NonlinearSolverState, params=NullParameters())
	initialize!(s, x)
	while true
	increase_iteration_number!(state)
	solver_step!(x, s, state, params)
	# update!(cache(s), state, x, nonlinearproblem(s), params) # this should not be necessary!
	status = NonlinearSolverStatus(state, cache(s), config(s))
	meets_stopping_criteria(status, iteration_number(state), config(s)) && break
	end
	status = NonlinearSolverStatus(state, cache(s), config(s))
	config(s).verbosity > 1 && print_status(status, iteration_number(state), config(s))
	warn_iteration_number(iteration_number(state), config(s))
	x
	end

for the nonlinear solver. This seems to be largely uniform, but the NonlinearSolverState is updated in solver_step!, whereas the OptimizerState is updated in solve! directly (see above).

The solver step in 85d665a:

SimpleSolvers.jl/src/nonlinear/nonlinear_solver.jl

Lines 114 to 132 in 85d665a

	function solver_step!(x::AbstractVector{T}, s::NonlinearSolver{T}, state::NonlinearSolverState{T}, params) where {T}
	direction!(s, x, params; state = state)
	# The following loop checks if the RHS contains any NaNs.
	# If so, the direction vector is reduced by a factor of LINESEARCH_NAN_FACTOR.
	update!(state, x, value!(value(state), nonlinearproblem(s), x, params), iteration_number(state))
	for _ in 1:LINESEARCH_NAN_MAX_ITERATIONS
	solution(cache(s)) .= solution(state) .+ direction(cache(s))
	value!(value(cache(s)), nonlinearproblem(s), solution(cache(s)), params)
	if any(isnan, value(cache(s)))
	(s.config.verbosity ≥ 2 && @warn "NaN detected in nonlinear solver. Reducing length of direction vector.")
	direction(cache(s)) .*= T(LINESEARCH_NAN_FACTOR)
	else
	break
	end
	end
	α = solve(linesearch_problem(s, state, params), linesearch(s))
	compute_new_iterate!(x, α, direction(cache(s)))
	x
	end

Originally posted by @benedict-96 in #61