Bug fix of dual init point computation in barrier

[yuwenchen95]

Description

Extend barrier initial-point handling for SOCP and fix augmented-path KKT assembly at initialization.

• Add ensure_initial_point_interior to push linear variables into the nonnegative orthant and SOC blocks into strict Lorentz cone interior; apply to x and z at the end of initial_point.
• Fix augmented init sign: remove erroneous diag.multiply_scalar(-1.0) so the first-call augmented build produces -(Q+D) on the primal block, matching augmented_multiply and the refactor path.
• Size augmented primal/dual RHS and solution vectors to max(n+m, device_augmented.n) for sparse SOC expansion, zero-padding extra entries.
• Enable initial-point iterative refinement for LP/QP augmented solves by seeding d_diag_ from host diag; skip IR for cone problems and direct-free linear variables where operator/factorization would disagree.
• Move primal, bound, and dual residual checks to after interior enforcement so diagnostics reflect the final starting point.
• Remove unused inv_sqrt_diag member and initialization.

Issue

Checklist

• I am familiar with the Contributing Guidelines.
• Testing
  • New or existing tests cover these changes
  • Added tests
  • Created an issue to follow-up
  • NA
• Documentation
  • The documentation is up to date with these changes
  • Added new documentation
  • NA

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📒 Files selected for processing (1)

• cpp/src/barrier/barrier.cu

🚧 Files skipped from review as they are similar to previous changes (1)

• cpp/src/barrier/barrier.cu

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📝 Walkthrough

Walkthrough

Changes

The barrier solver adds SOC-aware interior initialization and the Sturm/SeDuMi mu-based strategy. Diagonal preprocessing stores inv_diag directly, augmented vectors use computed dimensions, iterative refinement is restricted, and parameter documentation accepts option 2.

Barrier initialization

Layer / File(s)	Summary
Mu-based initial-point option cpp/src/math_optimization/solver_settings.cu, cpp/src/dual_simplex/simplex_solver_settings.hpp, python/cuopt_server/...	Allows barrier_dual_initial_point=2 and documents the Sturm/SeDuMi mu-based primal+dual initialization across C++ and Python interfaces.
Inverse diagonal preprocessing cpp/src/barrier/barrier.cu	Replaces inverse-square-root diagonal state and calculations with direct inverse-diagonal storage and device copying.
SOC-aware initial-point construction cpp/src/barrier/barrier.cu	Builds mu-based SOC initial points, sizes augmented vectors from the augmented system, restricts iterative refinement, enforces interiors, and recomputes residuals after shifts.

Estimated code review effort: 3 (Moderate) | ~25 minutes

Suggested labels: improvement

Suggested reviewers: rg20, ramakrishnap-nv, chris-maes

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title matches the main change: fixing barrier dual initial-point computation.
Description check	✅ Passed	The description is directly about the same barrier initial-point and SOC/KKT changes.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
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.

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⚠️ Outside diff range comments (2)

cpp/src/barrier/barrier.cu (1)

2187-2236: 🎯 Functional Correctness | 🟠 Major | ⚡ Quick win

SOC initial-point branches are unreachable for cone problems

data.has_cones() forces init_strategy to 2, and that branch returns immediately, so the later has_cones()/has_soc path in initial_point() never runs for SOCPs. That makes the new SOC interior-enforcement helper and the sparse-SOC aug_size path dead code here, and it also silently ignores any explicit barrier_dual_initial_point = 0/1 setting on cone problems.

🤖 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/barrier/barrier.cu` around lines 2187 - 2236, Update initial_point’s
init_strategy selection and early-return flow so cone problems do not
unconditionally force strategy 2. Preserve explicit barrier_dual_initial_point
values 0/1 for cone problems, and route those cases through the existing SOC
initialization/interior-enforcement and sparse-SOC aug_size logic; retain the
mu-based strategy 2 behavior when selected.

Source: Path instructions

python/cuopt_server/cuopt_server/tests/test_lp.py (1)

163-172: 🎯 Functional Correctness | 🟡 Minor | ⚡ Quick win

Add dual_initial_point=2 to the test matrix. The current @pytest.mark.parametrize list covers -1, 0, and 1, but not the new 2 value, so the mu-based path still isn’t exercised.

🤖 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 `@python/cuopt_server/cuopt_server/tests/test_lp.py` around lines 163 - 172,
Update the pytest parameterization for test_barrier_solver_options to include
dual_initial_point=2 alongside the existing -1, 0, and 1 values, ensuring the
mu-based path is exercised.

🤖 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.

Outside diff comments:
In `@cpp/src/barrier/barrier.cu`:
- Around line 2187-2236: Update initial_point’s init_strategy selection and
early-return flow so cone problems do not unconditionally force strategy 2.
Preserve explicit barrier_dual_initial_point values 0/1 for cone problems, and
route those cases through the existing SOC initialization/interior-enforcement
and sparse-SOC aug_size logic; retain the mu-based strategy 2 behavior when
selected.

In `@python/cuopt_server/cuopt_server/tests/test_lp.py`:
- Around line 163-172: Update the pytest parameterization for
test_barrier_solver_options to include dual_initial_point=2 alongside the
existing -1, 0, and 1 values, ensuring the mu-based path is exercised.

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Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

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📥 Commits

Reviewing files that changed from the base of the PR and between 5658d72 and 130b9a4.

📒 Files selected for processing (5)

• cpp/src/barrier/barrier.cu
• cpp/src/dual_simplex/simplex_solver_settings.hpp
• cpp/src/math_optimization/solver_settings.cu
• python/cuopt_server/cuopt_server/tests/test_lp.py
• python/cuopt_server/cuopt_server/utils/linear_programming/data_definition.py

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