Add customizable subsolver direction to ALM

Co-authored-by: Copilot <copilot@github.com>

Author: mateuszbaran

Changelog.md

@@ -6,6 +6,12 @@ The file was started with Version `0.4`.
 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).
 
+## [0.5.37] April 25, 2026
+
+### Added
+
+* Customizable subsolver direction update for augmented Lagrangian method.
+
 ## [0.5.36] April 24, 2026
 
 ### Added

Project.toml

@@ -1,6 +1,6 @@
 name = "Manopt"
 uuid = "0fc0a36d-df90-57f3-8f93-d78a9fc72bb5"
-version = "0.5.36"
+version = "0.5.37"
 authors = [{family-names = "Bergmann", given-names = "Ronny", alias = "kellertuer", city = "Trondheim", affiliation = "Norwegian University of Science and Technology", country = "NO", email = "manopt@ronnybergmann.net", orcid = "https://orcid.org/0000-0001-8342-7218", website = "https://ronnybergmann.net"}]
 
 [workspace]

src/solvers/augmented_Lagrangian_method.jl

@@ -325,6 +325,8 @@ $(_kwargs(:sub_problem; default = "`[`DefaultManoptProblem`](@ref)`(M, sub_objec
 $(_kwargs(:sub_state; default = "`[`QuasiNewtonState`](@ref)` ")), where more precisely
   as quasi newton method, the [`QuasiNewtonLimitedMemoryDirectionUpdate`](@ref) with [`InverseBFGS`](@ref) is used.
 * `sub_stopping_criterion::StoppingCriterion=`[`StopAfterIteration`](@ref)`(300)`$(_sc(:Any))[`StopWhenGradientNormLess`](@ref)`(ϵ)`$(_sc(:Any))[`StopWhenStepsizeLess`](@ref)`(1e-8)`,
+* `sub_direction_update::AbstractQuasiNewtonDirectionUpdate=`[`QuasiNewtonLimitedMemoryDirectionUpdate`](@ref)`(M, copy(M, p), InverseBFGS(), min(manifold_dimension(M), 30))`:
+  the direction update rule for the sub solver, where by default a limited memory quasi-Newton method with inverse BFGS update is used.
 
 
 For the `range`s of the constraints' gradient, other power manifold tangent space representations,
@@ -452,6 +454,9 @@ function augmented_Lagrangian_method!(
         sub_cost = AugmentedLagrangianCost(cmo, ρ, μ, λ),
         sub_grad = AugmentedLagrangianGrad(cmo, ρ, μ, λ),
         sub_kwargs = (;),
+        sub_direction_update::AbstractQuasiNewtonDirectionUpdate = QuasiNewtonLimitedMemoryDirectionUpdate(
+            M, copy(M, p), InverseBFGS(), min(manifold_dimension(M), 30)
+        ),
         sub_stopping_criterion::StoppingCriterion = StopAfterIteration(300) |
             StopWhenGradientNormLess(ϵ) |
             StopWhenStepsizeLess(1.0e-8),
@@ -460,9 +465,7 @@ function augmented_Lagrangian_method!(
                 M;
                 p = copy(M, p),
                 X = zero_vector(M, p),
-                direction_update = QuasiNewtonLimitedMemoryDirectionUpdate(
-                    M, copy(M, p), InverseBFGS(), min(manifold_dimension(M), 30)
-                ),
+                direction_update = sub_direction_update,
                 stopping_criterion = sub_stopping_criterion,
                 stepsize = default_stepsize(M, QuasiNewtonState),
                 sub_kwargs...,

test/solvers/test_augmented_lagrangian.jl

@@ -68,4 +68,32 @@ using LinearAlgebra: I, tr
         @test q isa Real
         @test f(M, q) < f(M, 4)
     end
+
+    @testset "Customizable subsolver direction update" begin
+        d = 20
+        M = Sphere(d - 1)
+        S = [ones(4)..., zeros(d - 4)...]
+        v0 = project(M, S)
+        Z = v0 * v0'
+        f(M, p) = -tr(transpose(p) * Z * p) / 2
+        grad_f(M, p) = project(M, p, -transpose.(Z) * p / 2 - Z * p / 2)
+        g(M, p) = -p # in other words p ≥ 0
+        mI = -Matrix{Float64}(I, d, d)
+        grad_g(M, p) = [project(M, p, mI[:, i]) for i in 1:d]
+        p0 = project(M, ones(d))
+        s = augmented_Lagrangian_method(
+            M,
+            f,
+            grad_f,
+            p0;
+            g = g,
+            grad_g = grad_g,
+            sub_direction_update = QuasiNewtonLimitedMemoryDirectionUpdate(
+                M, copy(M, p0), InverseBFGS(), 5
+            ),
+            stopping_criterion = StopAfterIteration(20),
+            return_state = true,
+        )
+        @test s.sub_state.direction_update.memory_s.capacity == 5
+    end
 end