Initial implementation of global optimisation

Author: eeshan9815

src/optimise1.jl

@@ -0,0 +1,52 @@
+using IntervalArithmetic, DataStructures
+
+import Base.isless
+
+struct IntervalMinima{T<:Real}
+    intval::Interval{T}
+    minima::T
+end
+
+function isless(a::IntervalMinima{T}, b::IntervalMinima{T}) where {T<:Real}
+    return isless(a.minima, b.minima)
+end
+
+function minimise1d(f::Function, x::Interval{T}; reltol=1e-3, abstol=1e-3) where {T<:Real}
+
+    Q = binary_minheap(IntervalMinima{T})
+
+    minima = f(interval(mid(x))).hi
+    arg_minima = Interval{T}[]
+
+    push!(Q, IntervalMinima(x, minima))
+
+    while !isempty(Q)
+
+        p = pop!(Q)
+
+        if p.minima > minima
+            continue
+        end
+        #
+        # if 0 ∉ ForwardDiff.derivative(f, p.intval)
+        #     continue
+        # end
+
+        # current_minima = f(p.intval).lo
+
+        current_minima = f(interval(mid(p.intval))).hi
+
+        if current_minima < minima
+            minima = current_minima
+        end
+
+        if diam(p.intval) < abstol
+            push!(arg_minima, p.intval)
+        else
+            x1, x2 = bisect(p.intval)
+            push!(Q, IntervalMinima(x1, f(x1).lo), IntervalMinima(x2, f(x2).lo))
+        end
+    end
+
+    return minima, arg_minima
+end