Adjust optimizer `update!` methods such that no state is needed

[benedict-96]

For updating the NewtonOptimizerCache (and others) we still need the NewtonOptimizerState:

SimpleSolvers.jl/src/optimization/newton_optimizer/newton_optimizer_cache.jl

Lines 63 to 67 in 69c6d5e

	function update!(cache::NewtonOptimizerCache, state::OptimizerState, x::AbstractVector)
	cache.x .= x
	direction(cache) .= cache.x - state.x̄
	cache
	end

Note

For the solvers this was tackled in #132.

[benedict-96]

In #132 the pertinent changes are in 8ccf3d6.
We now have (for the solver):

SimpleSolvers.jl/src/nonlinear/nonlinear_solver_state.jl

Lines 12 to 19 in b412a36

	mutable struct NonlinearSolverState{T,XT<:AbstractVector{T},YT<:AbstractVector{T}} <: AbstractSolverState
	iterations::Int
	x::XT
	x̄::XT
	y::YT
	ȳ::YT

For the optimizer we still have:

SimpleSolvers.jl/src/optimization/newton_optimizer/newton_optimizer_state.jl

Lines 14 to 19 in b412a36

	mutable struct NewtonOptimizerState{T, AT <: AbstractArray{T}, GT <: AbstractArray{T}} <: OptimizerState{T}
	x̄::AT
	ḡ::GT
	f̄::T
	iterations::Int

And for BFGS (DFP is the same):

SimpleSolvers.jl/src/optimization/iterative_hessians/bfgs/bfgs_state.jl

Lines 12 to 18 in b412a36

	mutable struct BFGSState{T, AT <: AbstractArray{T}, GT <: AbstractArray{T}, MT <: AbstractMatrix{T}} <: OptimizerState{T}
	x̄::AT
	ḡ::GT
	f̄::T
	Q::MT
	iterations::Int

[benedict-96]

For the NewtonOptimizer the relevant changes were made here: #141

For the optimizers that work with iterative Hessians, this probably requires additional planning.