Added golden section method

src/LineSearch.jl

@@ -22,6 +22,7 @@ function SciMLBase.reinit!(::AbstractLineSearchCache; kwargs...) end
 include("utils.jl")
 
 include("backtracking.jl")
+include("golden_section.jl")
 include("li_fukushima.jl")
 include("no_search.jl")
 include("robust_non_monotone.jl")
@@ -36,6 +37,7 @@ end
 export LineSearchSolution
 
 export BackTracking
+export GoldenSection
 export NoLineSearch, LiFukushimaLineSearch, RobustNonMonotoneLineSearch
 export LineSearchesJL
 

src/golden_section.jl

@@ -0,0 +1,82 @@
+"""
+    GoldenSection(; tol = 1e-7, maxiters = 100)
+
+A derivative-free line search that minimizes a unimodal function by successively 
+narrowing the interval containing the minimum using the golden ratio.
+"""
+@kwdef @concrete struct GoldenSection <: AbstractLineSearchAlgorithm
+    tol = 1.0e-7
+    maxiters::Int = 100
+end
+
+@concrete mutable struct GoldenSectionCache <: AbstractLineSearchCache
+    ϕ
+    f
+    p
+    u_cache
+    fu_cache
+    α
+    φ
+    resphi
+    stats <: Union{SciMLBase.NLStats, Nothing}
+    alg <: GoldenSection
+    maxiters::Int
+end
+
+function CommonSolve.init(
+        prob::AbstractNonlinearProblem, alg::GoldenSection, fu, u;
+        stats::Union{SciMLBase.NLStats, Nothing} = nothing, kwargs...
+    )
+    T = promote_type(eltype(fu), eltype(u))
+
+    φ = (sqrt(T(5)) + 1) / 2
+    resphi = 2 - φ
+
+    @bb u_cache = similar(u)
+    @bb fu_cache = similar(fu)
+
+    ϕ = @closure (f, p, u, du, α, u_cache, fu_cache) -> begin
+        @bb @. u_cache = u + α * du
+        fu_cache = evaluate_f!!(f, fu_cache, u_cache, p)
+        add_nf!(stats)
+        return @fastmath norm(fu_cache)^2 / 2
+    end
+
+    return GoldenSectionCache(
+        ϕ, prob.f, prob.p, u_cache, fu_cache, T(1), φ, resphi, stats, alg, alg.maxiters
+    )
+end
+
+function CommonSolve.solve!(cache::GoldenSectionCache, u, du)
+    T = promote_type(eltype(du), eltype(u))
+    ϕ = @closure α -> cache.ϕ(cache.f, cache.p, u, du, α, cache.u_cache, cache.fu_cache)
+
+    a, b = zero(T), T(cache.α)
+
+    x1 = a + cache.resphi * (b - a)
+    x2 = b - cache.resphi * (b - a)
+    f1, f2 = ϕ(x1), ϕ(x2)
+
+    for _ in 1:(cache.maxiters)
+        abs(b - a) ≤ cache.alg.tol && break
+        if f1 < f2
+            b = x2;  x2 = x1;  f2 = f1
+            x1 = a + cache.resphi * (b - a);  f1 = ϕ(x1)
+        else
+            a = x1;  x1 = x2;  f1 = f2
+            x2 = b - cache.resphi * (b - a);  f2 = ϕ(x2)
+        end
+    end
+
+    α_best = (a + b) / 2
+    return LineSearchSolution(α_best, ReturnCode.Success)
+end
+
+function SciMLBase.reinit!(
+        cache::GoldenSectionCache; p = missing, stats = missing, kwargs...
+    )
+    p !== missing && (cache.p = p)
+    stats !== missing && (cache.stats = stats)
+    cache.α = oftype(cache.α, true)
+    return cache
+end

test/custom_optimizer_tests.jl

@@ -117,6 +117,7 @@ end
             @testset "method: $(nameof(typeof(method)))" for method in (
                     LiFukushimaLineSearch(),
                     NoLineSearch(0.001),
+                    GoldenSection(; tol = 1.0e-4),
                     BackTracking(; order = Val(3), autodiff),
                     BackTracking(; order = Val(2), autodiff),
                 )
@@ -139,6 +140,7 @@ end
             @testset "method: $(nameof(typeof(method)))" for method in (
                     LiFukushimaLineSearch(),
                     NoLineSearch(0.001),
+                    GoldenSection(; tol = 1.0e-4),
                     BackTracking(; order = Val(3), autodiff),
                     BackTracking(; order = Val(2), autodiff),
                 )

test/root_finding_tests.jl

@@ -138,6 +138,7 @@ end
         @testset "method: $(nameof(typeof(method)))" for method in (
                 LiFukushimaLineSearch(),
                 NoLineSearch(0.5),
+                GoldenSection(; tol = 1.0e-4),
                 RobustNonMonotoneLineSearch(),
                 RobustNonMonotoneLineSearch(; M = 1), #strictly monotonous case
                 RobustNonMonotoneLineSearch(; M = 15),
@@ -171,6 +172,7 @@ end
         @testset "method: $(nameof(typeof(method)))" for method in (
                 LiFukushimaLineSearch(),
                 NoLineSearch(0.5),
+                GoldenSection(; tol = 1.0e-4),
                 RobustNonMonotoneLineSearch(),
                 RobustNonMonotoneLineSearch(; M = 1), #strictly monotonous case
                 RobustNonMonotoneLineSearch(; M = 15),