Checking for non-descent direction in qN (#361)

* Checking for non-descent direction in qN
* add test, fix tolerance

---------

Co-authored-by: Ronny Bergmann <[email protected]>

Changelog.md

@@ -5,7 +5,13 @@ All notable Changes to the Julia package `Manopt.jl` will be documented in this
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
-## [0.4.55] unreleased
+## [0.4.55] March 3, 2024
+
+### Added
+
+* Option `nondescent_direction_behavior` for quasi-Newton solvers.
+  By default it checks for non-descent direction which may not be handled well by
+  some stepsize selection algorithms.
 
 ### Fixed
 

Project.toml

@@ -1,7 +1,7 @@
 name = "Manopt"
 uuid = "0fc0a36d-df90-57f3-8f93-d78a9fc72bb5"
 authors = ["Ronny Bergmann <[email protected]>"]
-version = "0.4.54"
+version = "0.4.55"
 
 [deps]
 ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"

src/solvers/quasi_Newton.jl

@@ -60,6 +60,7 @@ mutable struct QuasiNewtonState{
     stop::SC
     X_old::T
     vector_transport_method::VT
+    nondescent_direction_behavior::Symbol
 end
 function QuasiNewtonState(
     M::AbstractManifold,
@@ -77,6 +78,7 @@ function QuasiNewtonState(
         retraction_method=retraction_method,
         vector_transport_method=vector_transport_method,
     ),
+    nondescent_direction_behavior::Symbol=:step_towards_negative_gradient,
     kwargs..., # collect but ignore rest to be more tolerant
 ) where {
     P,
@@ -101,6 +103,7 @@ function QuasiNewtonState(
         stopping_criterion,
         copy(M, p, initial_vector),
         vector_transport_method,
+        nondescent_direction_behavior,
     )
 end
 function get_message(qns::QuasiNewtonState)
@@ -200,6 +203,7 @@ The ``k``th iteration consists of
 * `stopping_criterion`:      ([`StopAfterIteration`](@ref)`(max(1000, memory_size)) | `[`StopWhenGradientNormLess`](@ref)`(1e-6)`)
   specify a [`StoppingCriterion`](@ref)
 * `vector_transport_method`: (`default_vector_transport_method(M, typeof(p))`) a vector transport to use.
+* `nondescent_direction_behavior`: (`:step_towards_negative_gradient`) specify how non-descent direction is handled. Can be either `:ignore` (in which case it is not checked if the selected direction is a descent one) or `:step_towards_negative_gradient` (in which case the direction is replaced with negative gradient).
 
 # Output
 
@@ -349,6 +353,13 @@ function step_solver!(mp::AbstractManoptProblem, qns::QuasiNewtonState, iter)
     M = get_manifold(mp)
     get_gradient!(mp, qns.X, qns.p)
     qns.direction_update(qns.η, mp, qns)
+    if qns.nondescent_direction_behavior === :step_towards_negative_gradient &&
+        real(inner(M, qns.p, qns.η, qns.X)) > 0
+        # reset direction if not a descent one
+        @warn "Computed direction is not a descent direction; resetting to negative gradient"
+        copyto!(M, qns.η, qns.X)
+        qns.η .*= -1
+    end
     α = qns.stepsize(mp, qns, iter, qns.η)
     copyto!(M, qns.p_old, get_iterate(qns))
     retract!(M, qns.p, qns.p, qns.η, α, qns.retraction_method)

test/solvers/test_convex_bundle_method.jl

@@ -166,7 +166,7 @@ using Manopt: sectional_curvature, ζ_1, ζ_2, close_point
         )
         q = get_solver_result(cbm_s)
         m = median(M, data)
-        @test distance(M, q, m) < 1e-2 #with default params this is not very precise
+        @test distance(M, q, m) < 1.5e-2 #with default params this is not very precise
         # tst the other stopping criterion mode
         q2 = convex_bundle_method(
             M,

test/solvers/test_quasi_Newton.jl

@@ -1,6 +1,18 @@
 using Manopt, Manifolds, Test
 using LinearAlgebra: I, eigvecs, tr, Diagonal
 
+struct QuasiNewtonGradientDirectionUpdate{VT<:AbstractVectorTransportMethod} <:
+       AbstractQuasiNewtonDirectionUpdate
+    vector_transport_method::VT
+end
+function (d::QuasiNewtonGradientDirectionUpdate)(mp, st)
+    return get_gradient(st)
+end
+function (d::QuasiNewtonGradientDirectionUpdate)(r, mp, st)
+    r .= get_gradient(st)
+    return r
+end
+
 @testset "Riemannian quasi-Newton Methods" begin
     @testset "Show & Status" begin
         M = Euclidean(4)
@@ -357,6 +369,22 @@ using LinearAlgebra: I, eigvecs, tr, Diagonal
         @test contains(qns.direction_update.message, "gradient")
     end
 
+    @testset "Broken direction update" begin
+        M = Euclidean(2)
+        p = [0.0, 1.0]
+        f(M, p) = sum(p .^ 2)
+        grad_f(M, p) = 2 * sum(p)
+        gmp = ManifoldGradientObjective(f, grad_f)
+        mp = DefaultManoptProblem(M, gmp)
+        qns = QuasiNewtonState(
+            M, p; direction_update=QuasiNewtonGradientDirectionUpdate(ParallelTransport())
+        )
+        @test_logs (
+            :warn,
+            "Computed direction is not a descent direction; resetting to negative gradient",
+        ) match_mode = :any solve!(mp, qns)
+    end
+
     @testset "A Circle example" begin
         M = Circle()
         data = [-π / 2, π / 4, 0.0, π / 4]