Missing docs

Author: avik-pal

docs/pages.jl

@@ -1,6 +1,7 @@
 # Put in a separate page so it can be used by SciMLDocs.jl
 
-pages = ["index.md",
+pages = [
+    "index.md",
     "Getting Started with Nonlinear Rootfinding in Julia" => "tutorials/getting_started.md",
     "Tutorials" => Any["tutorials/code_optimization.md",
         "tutorials/large_systems.md",

docs/src/basics/nonlinear_solution.md

@@ -1,6 +1,7 @@
 # [Nonlinear Solutions](@id solution)
 
 ```@docs
+SciMLBase.AbstractNonlinearSolution
 SciMLBase.NonlinearSolution
 ```
 

src/algorithms/lbroyden.jl

@@ -14,7 +14,8 @@ and line search.
     to `Val(10)`.
 """
 function LimitedMemoryBroyden(; max_resets::Int = 3, linesearch = NoLineSearch(),
-        threshold::Val = Val(10), reset_tolerance = nothing)
+        threshold::Union{Val, Int} = Val(10), reset_tolerance = nothing)
+    threshold isa Int && (threshold = Val(threshold))
     return ApproximateJacobianSolveAlgorithm{false, :LimitedMemoryBroyden}(; linesearch,
         descent = NewtonDescent(), update_rule = GoodBroydenUpdateRule(), max_resets,
         initialization = BroydenLowRankInitialization{_unwrap_val(threshold)}(threshold),

src/globalization/line_search.jl

@@ -157,10 +157,38 @@ function SciMLBase.solve!(cache::LineSearchesJLCache, u, du; kwargs...)
 end
 
 """
-    RobustNonMonotoneLineSearch(; gamma = 1 // 10000, sigma_0 = 1)
+    RobustNonMonotoneLineSearch(; gamma = 1 // 10000, sigma_0 = 1, M::Int = 10,
+        tau_min = 1 // 10, tau_max = 1 // 2, n_exp::Int = 2, maxiters::Int = 100,
+        η_strategy = (fn₁, n, uₙ, fₙ) -> fn₁ / n^2)
 
 Robust NonMonotone Line Search is a derivative free line search method from DF Sane
 [la2006spectral](@cite).
+
+### Keyword Arguments
+
+  - `M`: The monotonicity of the algorithm is determined by a this positive integer.
+    A value of 1 for `M` would result in strict monotonicity in the decrease of the L2-norm
+    of the function `f`. However, higher values allow for more flexibility in this reduction.
+    Despite this, the algorithm still ensures global convergence through the use of a
+    non-monotone line-search algorithm that adheres to the Grippo-Lampariello-Lucidi
+    condition. Values in the range of 5 to 20 are usually sufficient, but some cases may
+    call for a higher value of `M`. The default setting is 10.
+  - `gamma`: a parameter that influences if a proposed step will be accepted. Higher value
+    of `gamma` will make the algorithm more restrictive in accepting steps. Defaults to
+    `1e-4`.
+  - `tau_min`: if a step is rejected the new step size will get multiplied by factor, and
+    this parameter is the minimum value of that factor. Defaults to `0.1`.
+  - `tau_max`: if a step is rejected the new step size will get multiplied by factor, and
+    this parameter is the maximum value of that factor. Defaults to `0.5`.
+  - `n_exp`: the exponent of the loss, i.e. ``f_n=||F(x_n)||^{n\\_exp}``. The paper uses
+    `n_exp ∈ {1, 2}`. Defaults to `2`.
+  - `η_strategy`:  function to determine the parameter `η`, which enables growth
+    of ``||f_n||^2``. Called as `η = η_strategy(fn_1, n, x_n, f_n)` with `fn_1` initialized
+    as ``fn_1=||f(x_1)||^{n\\_exp}``, `n` is the iteration number, `x_n` is the current
+    `x`-value and `f_n` the current residual. Should satisfy ``η > 0`` and ``∑ₖ ηₖ < ∞``.
+    Defaults to ``fn_1 / n^2``.
+  - `maxiters`: the maximum number of iterations allowed for the inner loop of the
+    algorithm. Defaults to `100`.
 """
 @kwdef @concrete struct RobustNonMonotoneLineSearch <:
                         AbstractNonlinearSolveLineSearchAlgorithm