Update Manopt requirement from 0.5.25 to 0.5.25, 0.6 in /test in the all-julia-packages group across 1 directory

[dependabot]

Updates the requirements on Manopt to permit the latest version.
Updates Manopt to 0.6.1

Release notes

Sourced from Manopt's releases.

v0.6.1

Manopt v0.6.1

Diff since v0.6.0

Added

• the gradient sampling algorithm based on the paper by Hosseini and Uschmajew (#618)

Fixed

• Fix a typo in Riemannian Levenberg–Marquardt documentation. (#621)
• Fixed a coordinate-cache allocation in the VectorDifferentialFunction Jacobian-action path. (#622)

Merged pull requests:

• Gradient Sampling Algorithm (#618) (@​kellertuer)
• Bump actions/cache from 5 to 6 (#619) (@​dependabot[bot])
• Fix LM surrogate operator documentation (#621) (@​sChoiKr)
• Avoid coordinate cache allocation in VectorDifferentialFunction get_jacobian! (#622) (@​sChoiKr)

Closed issues:

• Add Riemannian gradient sampling algorithm (#272)
• Armijo linesearch does not allocate the right candidate point type (#533)
• Proposal: stable result interface or result-builder hook for downstream domain packages (#595)
• Question on Documentation for Levenberg-Marquadt Method (#620)
• LM operator path still materializes coordinates in nonlinear least-squares surrogate path (#623)

Changelog

Sourced from Manopt's changelog.

[0.6.1] July 4, 2026

Added

• the gradient sampling algorithm based on the paper by Hosseini and Uschmajew (#618)

Fixed

• Fix a typo in Riemannian Levenberg–Marquardt documentation. (#621)
• Fixed a coordinate-cache allocation in the VectorDifferentialFunction Jacobian-action path. (#622)

[0.6.0] June 24, 2026

This is a breaking change since the JuMP extension is dropped. We also unified a few of the internal solver state constructors.

Added

• A robustified version of the Riemannian Levenberg Marquardt algorithm (#617)
• An option to disable the warm start the conjugate residual currently does when used as a subsolver.
• 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. This resolves issue (#549). (#554)
• GeneralizedCauchyDirectionSubsolver 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)
• New stopping criteria: StopWhenRelativeAPosterioriCostChangeLessOrEqual and StopWhenProjectedNegativeGradientNormLess. (#554).
• HagerZhangLinesearch stepsize, a state-of-the-art line search for smooth objectives with cubic interpolation and adaptive Wolfe condition checking. (#554)
• Stopping criteria can now be initialized using initialize_stepsize!, similar to solvers. (#554)
• The ConjugateResidualState now has a warm_start= option when used multiple times, for example in every iteration as a subsolver, to reuse the last state from the previous run.

Changed

• In the Riemannian Levenberg Marquardt algorithmt the η parameter has been renamed to candidate_acceptance_threshold, β to damping_increase_factor and β_reduction to damping_reduction_factor. (#617)
• the constructor for the Levenberg-Marquardt state has been unified with the remaining states, to take the sub_problem and sub_state arguments as second and third positional arguments, respectively. (#617)
• the keyword initial_jacobian_f within LevenbergMarquardt is unified in naming to the residual values vector and called initial_jacobian_matrices. If you call LevenbergMarquardt with a single vector component, also a single matrix is allowed. (#617)
• an internal field of the solver state of Levenberg-Marqwuardt was called jacobian_f the same as the functions whose result it meant to cache if applicable. To distinguish both, the field is now called jacobian_matrices. (#617)
• the max_stepsize(M) on the SymmetricPositiveDefinite manifold was changed from returning Inf, which is the mathematical maximal stepsize to returning the square root of the maximum (floating point) value to avoid numerical instabilities.
• title of "How to define the cost in the embedding" tutorial (#615)

Fixed

• Fixed show methods of various state and stopping criteria to properly handle both repr and multiline printing (#569)
• Unified all show methods and their human readable analoga status_summary throughout the package (#569)
• Fixed some text descriptions of a few stopping criteria.
• unify naming of fields, debugDictionary of the debug state is now called debug_dictionary
• the NesterovRule now also stores an actual AbstractRetractionMethod instead of implicitly always using the default one.
• Line searches consistently respect stop_when_stepsize_exceeds keyword argument as a hard limit. (#554)
• StopWhenChangeLess falsely claimed to indicate convergence. This is now fixed. (#554)
• miscellaneous broken links in the documentation. (#614)

Removed

• The extension to JuMP. A replacement as a separate package is planned when the support for variables beyond vectors is more accessible in JuMP

... (truncated)

Commits

• ce33ca3 Gradient Sampling Algorithm (#618)
• 02e38dc Avoid coordinate cache allocation in VectorDifferentialFunction get_jacobian!...
• a86a1ea Fix LM surrogate operator documentation (#621)
• 0922d3f Bump actions/cache from 5 to 6 (#619)
• 4fb0485 Merge pull request #605 from JuliaManifolds/dev-0.6
• 2a8c21b remove one test of ismissing, that is no longer possible and set a changelog ...
• 8d9b3c1 Introduce a robust Levenberg-Marquardt (#617)
• da0ca0f Bump actions/checkout from 6 to 7 (#616)
• e316f08 Merge branch 'master' into dev-0.6
• e61de7e change title of embedding objective tutorial (#615)
• Additional commits viewable in compare view

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[ChrisRackauckas-Claude]

I investigated this update locally. As currently written, this PR does not actually test Manopt 0.6: the resolver keeps selecting Manopt v0.5.25 because released OptimizationManopt v1.3.3 restricts Manopt to 0.5.25-0.5.39. Forcing Manopt v0.6.1 in the test environment gives an unsatisfiable requirements error from OptimizationManopt.\n\nI opened the upstream prerequisite as SciML/Optimization.jl#1243. It widens OptimizationManopt's Manopt compat to 0.5.25, 0.6. Local verification:\n\n- OptimizationManopt tests passed with Manopt v0.6.1, Manifolds v0.11.28, and ManifoldsBase v2.4.0.\n- SymbolicAnalysis tests from this PR passed after developing that local OptimizationManopt branch into the test environment and forcing Manopt v0.6.1; this includes Core/dgp.jl | 28 pass.\n\nSo the downstream SymbolicAnalysis code appears compatible with Manopt 0.6 once OptimizationManopt permits it. This PR should wait for the upstream compat PR and an OptimizationManopt release, otherwise it will continue resolving the old Manopt line.