refactor: promote shared primitives to mathematical_optimization

[mlubin]

Moves linear algebra primitives and other shared utilities into the optimization namespace to reduce the need for using statements or namespace qualification introduced by #1446. Linear algebra goes into a new directory named cpp/src/linear_algebra and other utilities go into the pre-existing cpp/src/math_optimization directory.

No behavioral or API change; pure relocation.

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[mlubin]

/ok to test c7d9e22

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📥 Commits

Reviewing files that changed from the base of the PR and between c7d9e22 and b132224.

📒 Files selected for processing (86)

• cpp/src/CMakeLists.txt
• cpp/src/barrier/barrier.cu
• cpp/src/barrier/barrier.hpp
• cpp/src/barrier/conjugate_gradient.hpp
• cpp/src/barrier/cusparse_view.cu
• cpp/src/barrier/cusparse_view.hpp
• cpp/src/barrier/device_sparse_matrix.cu
• cpp/src/barrier/device_sparse_matrix.cuh
• cpp/src/barrier/iterative_refinement.hpp
• cpp/src/barrier/pinned_host_allocator.cu
• cpp/src/barrier/pinned_host_allocator.hpp
• cpp/src/barrier/sparse_cholesky.cuh
• cpp/src/barrier/translate_soc.hpp
• cpp/src/branch_and_bound/branch_and_bound.cpp
• cpp/src/branch_and_bound/branch_and_bound.hpp
• cpp/src/branch_and_bound/deterministic_workers.hpp
• cpp/src/branch_and_bound/diving_heuristics.cpp
• cpp/src/branch_and_bound/mip_node.hpp
• cpp/src/branch_and_bound/pseudo_costs.cpp
• cpp/src/branch_and_bound/pseudo_costs.hpp
• cpp/src/branch_and_bound/symmetry.hpp
• cpp/src/branch_and_bound/worker.hpp
• cpp/src/branch_and_bound/worker_pool.hpp
• cpp/src/cuts/cuts.cpp
• cpp/src/cuts/cuts.hpp
• cpp/src/dual_simplex/CMakeLists.txt
• cpp/src/dual_simplex/basis_solves.cpp
• cpp/src/dual_simplex/basis_solves.hpp
• cpp/src/dual_simplex/basis_updates.hpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.cpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.hpp
• cpp/src/dual_simplex/crossover.cpp
• cpp/src/dual_simplex/crossover.hpp
• cpp/src/dual_simplex/folding.cpp
• cpp/src/dual_simplex/folding.hpp
• cpp/src/dual_simplex/initial_basis.cpp
• cpp/src/dual_simplex/initial_basis.hpp
• cpp/src/dual_simplex/phase1.cpp
• cpp/src/dual_simplex/phase1.hpp
• cpp/src/dual_simplex/phase2.cpp
• cpp/src/dual_simplex/phase2.hpp
• cpp/src/dual_simplex/presolve.cpp
• cpp/src/dual_simplex/presolve.hpp
• cpp/src/dual_simplex/primal.cpp
• cpp/src/dual_simplex/primal.hpp
• cpp/src/dual_simplex/right_looking_lu.cpp
• cpp/src/dual_simplex/right_looking_lu.hpp
• cpp/src/dual_simplex/scaling.cpp
• cpp/src/dual_simplex/scaling.hpp
• cpp/src/dual_simplex/simplex_solver_settings.hpp
• cpp/src/dual_simplex/singletons.cpp
• cpp/src/dual_simplex/singletons.hpp
• cpp/src/dual_simplex/solution.hpp
• cpp/src/dual_simplex/solve.cpp
• cpp/src/dual_simplex/solve.hpp
• cpp/src/dual_simplex/triangle_solve.hpp
• cpp/src/dual_simplex/user_problem.hpp
• cpp/src/linear_algebra/CMakeLists.txt
• cpp/src/linear_algebra/dense_matrix.hpp
• cpp/src/linear_algebra/dense_vector.hpp
• cpp/src/linear_algebra/sort_csr.cuh
• cpp/src/linear_algebra/sparse_matrix.cpp
• cpp/src/linear_algebra/sparse_matrix.hpp
• cpp/src/linear_algebra/sparse_vector.cpp
• cpp/src/linear_algebra/sparse_vector.hpp
• cpp/src/linear_algebra/vector_math.cpp
• cpp/src/linear_algebra/vector_math.cuh
• cpp/src/linear_algebra/vector_math.hpp
• cpp/src/math_optimization/CMakeLists.txt
• cpp/src/math_optimization/tic_toc.cpp
• cpp/src/math_optimization/tic_toc.hpp
• cpp/src/math_optimization/types.hpp
• cpp/src/mip_heuristics/diversity/lns/rins.cu
• cpp/src/mip_heuristics/diversity/recombiners/sub_mip.cuh
• cpp/src/mip_heuristics/feasibility_jump/fj_cpu.cu
• cpp/src/mip_heuristics/presolve/conflict_graph/clique_table.cu
• cpp/src/mip_heuristics/presolve/semi_continuous.cu
• cpp/src/mip_heuristics/problem/problem.cu
• cpp/src/mip_heuristics/solve.cu
• cpp/src/pdlp/solve.cu
• cpp/src/pdlp/translate.hpp
• cpp/tests/dual_simplex/unit_tests/right_looking_ldlt.cpp
• cpp/tests/dual_simplex/unit_tests/solve.cpp
• cpp/tests/dual_simplex/unit_tests/solve_barrier.cu
• cpp/tests/mip/cuts_test.cu
• cpp/tests/socp/general_quadratic_test.cu

💤 Files with no reviewable changes (1)

• cpp/src/dual_simplex/CMakeLists.txt

✅ Files skipped from review due to trivial changes (28)

• cpp/src/dual_simplex/singletons.hpp
• cpp/src/barrier/pinned_host_allocator.hpp
• cpp/src/CMakeLists.txt
• cpp/src/dual_simplex/triangle_solve.hpp
• cpp/src/dual_simplex/scaling.hpp
• cpp/src/dual_simplex/folding.hpp
• cpp/src/dual_simplex/solution.hpp
• cpp/src/dual_simplex/folding.cpp
• cpp/src/dual_simplex/basis_solves.cpp
• cpp/src/mip_heuristics/presolve/semi_continuous.cu
• cpp/src/dual_simplex/initial_basis.hpp
• cpp/src/branch_and_bound/diving_heuristics.cpp
• cpp/src/dual_simplex/basis_solves.hpp
• cpp/src/dual_simplex/crossover.hpp
• cpp/tests/dual_simplex/unit_tests/right_looking_ldlt.cpp
• cpp/src/dual_simplex/phase2.cpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.hpp
• cpp/src/dual_simplex/basis_updates.hpp
• cpp/src/dual_simplex/presolve.cpp
• cpp/src/dual_simplex/phase2.hpp
• cpp/src/dual_simplex/presolve.hpp
• cpp/src/math_optimization/tic_toc.cpp
• cpp/src/branch_and_bound/mip_node.hpp
• cpp/src/dual_simplex/right_looking_lu.hpp
• cpp/src/dual_simplex/right_looking_lu.cpp
• cpp/src/dual_simplex/simplex_solver_settings.hpp
• cpp/src/dual_simplex/scaling.cpp
• cpp/src/linear_algebra/sparse_vector.cpp

🚧 Files skipped from review as they are similar to previous changes (54)

• cpp/src/math_optimization/CMakeLists.txt
• cpp/src/dual_simplex/primal.hpp
• cpp/src/dual_simplex/user_problem.hpp
• cpp/src/branch_and_bound/worker_pool.hpp
• cpp/src/linear_algebra/CMakeLists.txt
• cpp/src/mip_heuristics/diversity/lns/rins.cu
• cpp/src/barrier/cusparse_view.hpp
• cpp/src/dual_simplex/phase1.cpp
• cpp/src/mip_heuristics/feasibility_jump/fj_cpu.cu
• cpp/src/dual_simplex/phase1.hpp
• cpp/src/mip_heuristics/diversity/recombiners/sub_mip.cuh
• cpp/src/dual_simplex/initial_basis.cpp
• cpp/src/dual_simplex/singletons.cpp
• cpp/src/linear_algebra/sparse_matrix.cpp
• cpp/src/dual_simplex/primal.cpp
• cpp/src/math_optimization/types.hpp
• cpp/src/dual_simplex/solve.hpp
• cpp/src/branch_and_bound/worker.hpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.cpp
• cpp/src/barrier/barrier.hpp
• cpp/src/barrier/pinned_host_allocator.cu
• cpp/src/mip_heuristics/presolve/conflict_graph/clique_table.cu
• cpp/src/math_optimization/tic_toc.hpp
• cpp/src/branch_and_bound/branch_and_bound.hpp
• cpp/src/barrier/cusparse_view.cu
• cpp/src/linear_algebra/sort_csr.cuh
• cpp/src/barrier/conjugate_gradient.hpp
• cpp/src/linear_algebra/dense_matrix.hpp
• cpp/src/branch_and_bound/deterministic_workers.hpp
• cpp/tests/mip/cuts_test.cu
• cpp/src/barrier/device_sparse_matrix.cu
• cpp/tests/socp/general_quadratic_test.cu
• cpp/tests/dual_simplex/unit_tests/solve.cpp
• cpp/src/mip_heuristics/problem/problem.cu
• cpp/src/branch_and_bound/branch_and_bound.cpp
• cpp/src/linear_algebra/dense_vector.hpp
• cpp/src/dual_simplex/crossover.cpp
• cpp/tests/dual_simplex/unit_tests/solve_barrier.cu
• cpp/src/branch_and_bound/pseudo_costs.cpp
• cpp/src/mip_heuristics/solve.cu
• cpp/src/linear_algebra/sparse_matrix.hpp
• cpp/src/linear_algebra/vector_math.hpp
• cpp/src/branch_and_bound/symmetry.hpp
• cpp/src/linear_algebra/sparse_vector.hpp
• cpp/src/branch_and_bound/pseudo_costs.hpp
• cpp/src/barrier/device_sparse_matrix.cuh
• cpp/src/linear_algebra/vector_math.cpp
• cpp/src/linear_algebra/vector_math.cuh
• cpp/src/barrier/translate_soc.hpp
• cpp/src/pdlp/solve.cu
• cpp/src/cuts/cuts.cpp
• cpp/src/barrier/barrier.cu
• cpp/src/barrier/sparse_cholesky.cuh
• cpp/src/cuts/cuts.hpp

---

📝 Walkthrough

Walkthrough

The PR adds linear_algebra and math_optimization sources to the build, moves shared timing and scalar utilities into cuopt::mathematical_optimization, and updates barrier, dual simplex, cuts, branch-and-bound, MIP, PDLP, and tests to the relocated APIs.

Changes

Namespace and utility migration

Layer / File(s)	Summary
Math optimization build and timing cpp/src/CMakeLists.txt, cpp/src/math_optimization/*	The build registers the new math-optimization sources, and tic/toc plus the shared scalar types are declared under cuopt::mathematical_optimization.
Linear algebra API relocation cpp/src/linear_algebra/*	The linear-algebra build, headers, and implementations move into cuopt::mathematical_optimization, and the dense, sparse, vector, norm, and CSR-sorting APIs switch to the new non-simplex types.
Barrier solver core cpp/src/barrier/barrier.*, cpp/src/barrier/conjugate_gradient.hpp, cpp/src/barrier/iterative_refinement.hpp	Barrier solver entry points, conjugate-gradient helpers, iterative refinement, and residual logging switch to the relocated vector math and timing helpers, and the public create_Q signature uses the unqualified CSC matrix type.
Barrier matrix adapters cpp/src/barrier/cusparse_view.*, cpp/src/barrier/device_sparse_matrix.*, cpp/src/barrier/pinned_host_allocator.*	The CSC/CSR device wrappers and pinned-host allocator retarget their matrix types and namespace scopes to the new linear-algebra headers.
Barrier factorization and SOC translation cpp/src/barrier/sparse_cholesky.cuh, cpp/src/barrier/translate_soc.hpp, cpp/tests/socp/general_quadratic_test.cu	Sparse Cholesky and SOC translation switch their matrix, sparse-vector, and timing types to the relocated APIs, and the SOC test updates its matrix and inf references.
Dual simplex migration cpp/src/dual_simplex/*, cpp/tests/dual_simplex/unit_tests/*	Dual simplex headers, implementations, CMake wiring, and unit tests replace dual_simplex includes with the new headers and switch public CSR and timing references to the new namespaces.
Branch-and-bound migration cpp/src/branch_and_bound/*	Branch-and-bound, pseudo-cost, symmetry, worker, and deterministic coordinator code update their CSR matrix, inf, and tic/toc usage to the relocated headers.
Cuts and cut generation cpp/src/cuts/*, cpp/tests/mip/cuts_test.cu	Cut interfaces, generators, and the cuts test switch to the new CSR and sparse-vector types, and variable_bounds_t changes its infinity-branch logic.
MIP heuristics and PDLP cpp/src/mip_heuristics/*, cpp/src/pdlp/*	MIP heuristics and PDLP translation/solve code replace the old sort, timing, matrix, and norm helpers with the relocated APIs.

Estimated code review effort

🎯 4 (Complex) | ⏱️ ~60 minutes

Possibly related PRs

• NVIDIA/cuopt#500: Both PRs touch the barrier solver’s quadratic-objective plumbing, including barrier_solver_t::create_Q(...) in cpp/src/barrier/barrier.hpp.
• NVIDIA/cuopt#1290: Both PRs touch the SOCP/quadratic-to-cone conversion path in cpp/src/barrier/translate_soc.hpp.
• NVIDIA/cuopt#1446: Both PRs cover the same barrier and linear-algebra namespace reorganization across cpp/src/barrier/* and cpp/src/linear_algebra/*.

Suggested reviewers

• bdice
• kaatish
• nguidotti

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Docstring Coverage	⚠️ Warning	Docstring coverage is 9.09% which is insufficient. The required threshold is 80.00%.	Write docstrings for the functions missing them to satisfy the coverage threshold.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title concisely summarizes the namespace refactor and shared primitive promotion described by the diff.
Description check	✅ Passed	The description matches the change set, describing the relocation of shared linear algebra and utility code into the optimization namespace.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

---

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[coderabbitai]

🧹 Nitpick comments (1)

cpp/src/linear_algebra/vector_math.cuh (1)

100-113: 🎯 Functional Correctness | 🔵 Trivial | ⚡ Quick win

Use cuda::std::abs in the device lambda.

The new transform uses unqualified abs, while the existing device reducer above uses cuda::std::abs; making this explicit avoids host/device overload surprises for floating-point f_t.

Proposed fix

-    [] __host__ __device__(f_t val) { return abs(val); },
+    [] __host__ __device__(f_t val) { return cuda::std::abs(val); },

As per coding guidelines, “Prevent numerical instability (overflow, underflow, precision loss) producing wrong results.”

🤖 Prompt for AI Agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@cpp/src/linear_algebra/vector_math.cuh` around lines 100 - 113, The device
lambda in vector_norm_inf currently uses unqualified abs, which can pick the
wrong overload for floating-point device code. Update the transform_reduce
lambda to use cuda::std::abs consistently with the rest of the file, and keep
the change localized to vector_norm_inf so the maximum absolute value reduction
remains explicit and device-safe.

Source: Coding guidelines

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Nitpick comments:
In `@cpp/src/linear_algebra/vector_math.cuh`:
- Around line 100-113: The device lambda in vector_norm_inf currently uses
unqualified abs, which can pick the wrong overload for floating-point device
code. Update the transform_reduce lambda to use cuda::std::abs consistently with
the rest of the file, and keep the change localized to vector_norm_inf so the
maximum absolute value reduction remains explicit and device-safe.

---

ℹ️ Review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Enterprise

Run ID: cf69ebbe-a488-4896-8cda-48cf83f0eb13

📥 Commits

Reviewing files that changed from the base of the PR and between 4e87bf7 and c7d9e22.

📒 Files selected for processing (86)

• cpp/src/CMakeLists.txt
• cpp/src/barrier/barrier.cu
• cpp/src/barrier/barrier.hpp
• cpp/src/barrier/conjugate_gradient.hpp
• cpp/src/barrier/cusparse_view.cu
• cpp/src/barrier/cusparse_view.hpp
• cpp/src/barrier/device_sparse_matrix.cu
• cpp/src/barrier/device_sparse_matrix.cuh
• cpp/src/barrier/iterative_refinement.hpp
• cpp/src/barrier/pinned_host_allocator.cu
• cpp/src/barrier/pinned_host_allocator.hpp
• cpp/src/barrier/sparse_cholesky.cuh
• cpp/src/barrier/translate_soc.hpp
• cpp/src/branch_and_bound/branch_and_bound.cpp
• cpp/src/branch_and_bound/branch_and_bound.hpp
• cpp/src/branch_and_bound/deterministic_workers.hpp
• cpp/src/branch_and_bound/diving_heuristics.cpp
• cpp/src/branch_and_bound/mip_node.hpp
• cpp/src/branch_and_bound/pseudo_costs.cpp
• cpp/src/branch_and_bound/pseudo_costs.hpp
• cpp/src/branch_and_bound/symmetry.hpp
• cpp/src/branch_and_bound/worker.hpp
• cpp/src/branch_and_bound/worker_pool.hpp
• cpp/src/cuts/cuts.cpp
• cpp/src/cuts/cuts.hpp
• cpp/src/dual_simplex/CMakeLists.txt
• cpp/src/dual_simplex/basis_solves.cpp
• cpp/src/dual_simplex/basis_solves.hpp
• cpp/src/dual_simplex/basis_updates.hpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.cpp
• cpp/src/dual_simplex/bound_flipping_ratio_test.hpp
• cpp/src/dual_simplex/crossover.cpp
• cpp/src/dual_simplex/crossover.hpp
• cpp/src/dual_simplex/folding.cpp
• cpp/src/dual_simplex/folding.hpp
• cpp/src/dual_simplex/initial_basis.cpp
• cpp/src/dual_simplex/initial_basis.hpp
• cpp/src/dual_simplex/phase1.cpp
• cpp/src/dual_simplex/phase1.hpp
• cpp/src/dual_simplex/phase2.cpp
• cpp/src/dual_simplex/phase2.hpp
• cpp/src/dual_simplex/presolve.cpp
• cpp/src/dual_simplex/presolve.hpp
• cpp/src/dual_simplex/primal.cpp
• cpp/src/dual_simplex/primal.hpp
• cpp/src/dual_simplex/right_looking_lu.cpp
• cpp/src/dual_simplex/right_looking_lu.hpp
• cpp/src/dual_simplex/scaling.cpp
• cpp/src/dual_simplex/scaling.hpp
• cpp/src/dual_simplex/simplex_solver_settings.hpp
• cpp/src/dual_simplex/singletons.cpp
• cpp/src/dual_simplex/singletons.hpp
• cpp/src/dual_simplex/solution.hpp
• cpp/src/dual_simplex/solve.cpp
• cpp/src/dual_simplex/solve.hpp
• cpp/src/dual_simplex/triangle_solve.hpp
• cpp/src/dual_simplex/user_problem.hpp
• cpp/src/linear_algebra/CMakeLists.txt
• cpp/src/linear_algebra/dense_matrix.hpp
• cpp/src/linear_algebra/dense_vector.hpp
• cpp/src/linear_algebra/sort_csr.cuh
• cpp/src/linear_algebra/sparse_matrix.cpp
• cpp/src/linear_algebra/sparse_matrix.hpp
• cpp/src/linear_algebra/sparse_vector.cpp
• cpp/src/linear_algebra/sparse_vector.hpp
• cpp/src/linear_algebra/vector_math.cpp
• cpp/src/linear_algebra/vector_math.cuh
• cpp/src/linear_algebra/vector_math.hpp
• cpp/src/math_optimization/CMakeLists.txt
• cpp/src/math_optimization/tic_toc.cpp
• cpp/src/math_optimization/tic_toc.hpp
• cpp/src/math_optimization/types.hpp
• cpp/src/mip_heuristics/diversity/lns/rins.cu
• cpp/src/mip_heuristics/diversity/recombiners/sub_mip.cuh
• cpp/src/mip_heuristics/feasibility_jump/fj_cpu.cu
• cpp/src/mip_heuristics/presolve/conflict_graph/clique_table.cu
• cpp/src/mip_heuristics/presolve/semi_continuous.cu
• cpp/src/mip_heuristics/problem/problem.cu
• cpp/src/mip_heuristics/solve.cu
• cpp/src/pdlp/solve.cu
• cpp/src/pdlp/translate.hpp
• cpp/tests/dual_simplex/unit_tests/right_looking_ldlt.cpp
• cpp/tests/dual_simplex/unit_tests/solve.cpp
• cpp/tests/dual_simplex/unit_tests/solve_barrier.cu
• cpp/tests/mip/cuts_test.cu
• cpp/tests/socp/general_quadratic_test.cu

💤 Files with no reviewable changes (1)

• cpp/src/dual_simplex/CMakeLists.txt

[mlubin]

/ok to test b132224