Generalized Cauchy point and box constraints

Changelog.md

@@ -6,10 +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).
 
-## [Unreleased]
+## Unreleased
 
 ### Added
 
+* `nonpositive_curvature_behavior` for `QuasiNewtonLimitedMemoryDirectionUpdate` that determines how transported (y, s) vector pairs are treated after transport; if their inner product gets too low, it may lead to non-positive-definite Hessians which needs to be avoided. (#554)
+* `GCPFinder` for handling direction selection in the presence of box (`Hyperrectangle`) constraints in quasi-Newton methods. This allows for L-BFGS-B-style box constraint handling. (#554)
 * add keyword argument `is_feasible_error` to `interior_point_Newton` to control how to handle infeasible starting points (#556)
 * add keyword argument `at_init` to some debug options to control whether they print already at the initialisation and hence before the first iteration (#552)
 
@@ -29,7 +31,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 * Removed `atol` from `DebugFeasibility` and instead use the one newly added `atol` from the `ConstrainedManifoldObjective`. (#546)
 * Move from CompatHelper to dependabot to keep track of dependency updates in Julia packages. (#547)
 * moved the `ManoptTestSuite` module to a sub module `Manopt.Test` within `Manopt.jl`,
-so it can be easier reused by others as well (#550)
+  so it can be easier reused by others as well (#550)
 * moved to using a `Project.toml` for tests and an overall `[Workspace]`.
   This also allows finally to run single test files without installing all packages manually, but instead just switching to and instantiating the test environment. (#550)
 * for compatibility, state also `[source]` entries consistently in the sub `Project.toml` files. (#550)

docs/src/references.bib

@@ -260,6 +260,34 @@ @book{Boumal:2023
     ISBN      = {978-1-00-916616-4}
 }
 
+@article{ByrdNocedalSchnabel:1994,
+	title = {Representations of quasi-{Newton} matrices and their use in limited memory methods},
+	volume = {63},
+	issn = {1436-4646},
+	doi = {10.1007/BF01582063},
+	number = {1},
+	urldate = {2025-09-06},
+	journal = {Mathematical Programming},
+	author = {Byrd, Richard H. and Nocedal, Jorge and Schnabel, Robert B.},
+	month = jan,
+	year = {1994},
+	pages = {129--156},
+}
+
+@article{ByrdLuNocedalZhu:1995,
+	title = {A {Limited} {Memory} {Algorithm} for {Bound} {Constrained} {Optimization}},
+	volume = {16},
+	issn = {1064-8275},
+	doi = {10.1137/0916069},
+	number = {5},
+	journal = {SIAM Journal on Scientific Computing},
+	author = {Byrd, Richard H. and Lu, Peihuang and Nocedal, Jorge and Zhu, Ciyou},
+	month = sep,
+	year = {1995},
+	note = {Publisher: Society for Industrial and Applied Mathematics},
+	pages = {1190--1208},
+}
+
 % --- C
 %
 %

ext/ManoptManifoldsExt/manifold_functions.jl

@@ -8,6 +8,19 @@ Manopt.default_point_distance(::Euclidean, p) = norm(p, Inf)
 
 Manopt.default_vector_norm(::Euclidean, p, X) = norm(p, Inf)
 
+
+Manopt.get_bounds_index(M::Hyperrectangle) = eachindex(M.lb)
+
+function Manopt.get_bound_t(M::Hyperrectangle, p, d, i)
+    if d[i] > 0
+        return (M.ub[i] - p[i]) / d[i]
+    elseif d[i] < 0
+        return (M.lb[i] - p[i]) / d[i]
+    else
+        return Inf
+    end
+end
+
 """
     max_stepsize(M::TangentBundle, p)
 
@@ -169,3 +182,21 @@ function reflect!(
     X .*= -1
     return retract!(M, q, p, X, retraction_method)
 end
+
+function Manopt.set_bound_t_at_index!(::Hyperrectangle, p_cp, t, d, i)
+    p_cp[i] += t * d[i]
+    return p_cp
+end
+
+function Manopt.set_bound_at_index!(M::Hyperrectangle, p_cp, d, i)
+    p_cp[i] = d[i] > 0 ? M.ub[i] : M.lb[i]
+    d[i] = 0
+    return p_cp
+end
+
+function Manopt.bound_direction_tweak!(::Hyperrectangle, d_out, d, p, p_cp)
+    return d_out .= p_cp .- p
+end
+
+Manopt.requires_gcp(::Hyperrectangle) = true
+Manopt.get_at_bound_index(::Hyperrectangle, X, b) = X[b]

src/Manopt.jl

@@ -13,11 +13,11 @@ import LinearAlgebra: reflect!
 import ManifoldsBase: embed!, plot_slope, prepare_check_result, find_best_slope_window
 import ManifoldsBase: base_manifold, base_point, get_basis
 import ManifoldsBase: project, project!
-import LinearAlgebra: cross
+import LinearAlgebra: cross, LowerTriangular
 using ColorSchemes
 using ColorTypes
 using Colors
-using DataStructures: CircularBuffer, capacity, length, push!, size, isfull
+using DataStructures: BinaryHeap, CircularBuffer, capacity, length, push!, size, isfull
 using Dates: Millisecond, Nanosecond, Period, canonicalize, value
 using LinearAlgebra:
     cond,
@@ -567,6 +567,7 @@ export StopAfter,
     StopWhenGradientChangeLess,
     StopWhenGradientMappingNormLess,
     StopWhenGradientNormLess,
+    StopWhenProjectedMinusGradientNormLess,
     StopWhenFirstOrderProgress,
     StopWhenIterateNaN,
     StopWhenKKTResidualLess,

src/helpers/LineSearchesTypes.jl

@@ -14,7 +14,8 @@ Wrapper for line searches available in the `LineSearches.jl` library.
 
 Wrap `linesearch` (for example [`HagerZhang`](https://julianlsolvers.github.io/LineSearches.jl/latest/reference/linesearch.html#LineSearches.HagerZhang)
 or [`MoreThuente`](https://julianlsolvers.github.io/LineSearches.jl/latest/reference/linesearch.html#LineSearches.MoreThuente)).
-The initial step selection from Linesearches.jl is not yet supported and the value 1.0 is used.
+The initial step selection from Linesearches.jl is not yet supported and `initial_guess` is
+always used (by default [`ConstantInitialGuess`](@ref)).
 
 # Keyword Arguments