convex hull

src/polytope_oracles.jl

@@ -216,3 +216,26 @@ function compute_extreme_point(
     v[idx] = ifelse(lower, lmo.lower_bounds[idx], lmo.upper_bounds[idx])
     return v
 end
+
+"""
+    ConvexHullOracle{AT,VT}
+
+Convex hull of a finite number of vertices of type `AT`, stored in a vector of type `VT`.
+"""
+struct ConvexHullOracle{AT, VT <: AbstractVector{AT}}
+    vertices::VT
+end
+
+function compute_extreme_point(lmo::ConvexHullOracle{AT}, direction; v=nothing, kwargs...) where {AT}
+    T = promote_type(eltype(direction), eltype(AT))
+    best_val = T(Inf)
+    best_vertex = first(lmo.vertices)
+    for vertex in lmo.vertices
+        val = dot(vertex, direction)
+        if val < best_val
+            best_val = val
+            best_vertex = vertex
+        end
+    end
+    return best_vertex
+end

test/lmo.jl

@@ -788,3 +788,20 @@ end
     xv = JuMP.value.(x)
     @test dot(xv, d) ≈ dot(v, d) atol=1e-5*n
 end
+
+@testset "Convex hull" begin
+    lmo = FrankWolfe.ConvexHullOracle([
+        [1, 0, 0],
+        [0, 1, 0],
+        [0, 0, 1],
+    ])
+    for _ in 1:100
+        d = randn(3)
+        v = FrankWolfe.compute_extreme_point(lmo, d)
+        v_simplex = FrankWolfe.compute_extreme_point(FrankWolfe.ProbabilitySimplexOracle(1), d)
+        @test v == v_simplex
+    end
+    d = zeros(3)
+    v = FrankWolfe.compute_extreme_point(lmo, d)
+    @test v == lmo.vertices[1]
+end