Add backtracking line search

Project.toml

@@ -3,6 +3,9 @@ uuid = "87fe0de2-c867-4266-b59a-2f0a94fc965b"
 authors = ["Vaibhav Dixit <[email protected]> and contributors"]
 version = "1.0.0-DEV"
 
+[deps]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
 [compat]
 julia = "1.9"
 

src/Backtracking.jl

@@ -0,0 +1,58 @@
+#=
+Backtracking line search implementation
+=#
+
+#=
+Input parameters:
+    - x: current iterate
+    - g: gradient 
+    - α: initial step size
+    - p: descent direction
+    - f: function evaluation
+=#
+
+mutable struct Backtracking{X, F, A}
+    x::X
+    g::X
+    p::X
+    f::F
+    α::A
+end
+
+# Determine step size by backtracking line search
+function Backtracking(backtrack::Backtracking)
+    # Setup (Function information)
+    x = backtrack.x
+    g = backtrack.g
+    α = backtrack.α
+    p = backtrack.p
+    f = backtrack.f
+
+    # Setup (Parameters)
+    c1 = 1e-4
+    β = 0.5
+    iterations = 1_000
+
+    ϕ_0 = f(x)
+    ϕ_α = f(x + α*p)
+    iteration = 0
+
+    # Backtracking line search
+    while ϕ_α > ϕ_0 + c1 * α * g * p
+        # Increment the number of steps we've had to perform
+        iteration += 1
+
+        # Ensure termination
+        if iteration > iterations
+            throw(LineSearchException("Linesearch failed to converge, reached maximum iterations $(iterations).", α))
+        end
+
+        # Decrease the step-size
+        α = β * α
+
+        # Update function value at new iterate
+        ϕ_α = f(x + α*p)
+    end
+
+    return α
+end

src/LineSearch.jl

@@ -2,4 +2,8 @@ module LineSearch
 
 # Write your package code here.
 
-end
+include("Backtracking.jl")
+
+export Backtracking
+
+end

test/runtests.jl

@@ -3,4 +3,21 @@ using Test
 
 @testset "LineSearch.jl" begin
     # Write your tests here.
+
+    # Test1: Quadratic function
+    f(u) = u*u
+    x = 1
+    g = 2
+    p = -g 
+    α = 1
+
+    # Create a Backtracking object
+    my_b = Backtracking(x, g, p, f, α)
+    α = Backtracking(my_b)
+
+    print(α)
+
+    # Test alpha
+    @test α == 0.5
+    @test 0 == 0
 end