Add comprehensive SDP test suite and evaluation harness

[mpf]

Summary

This PR adds a complete test suite for the SDP (semidefinite programming) solver implementation, including 40+ unit tests covering core SDP operations, standard problem instances, edge cases, and an evaluation harness for systematic validation.

Key Changes

• New test file test/sdp_tests.jl (583 lines): Comprehensive test suite organized into sections:

  • Unit tests for vecm/mat round-trip and inner product preservation
  • VecCongurance block operations (multiplication, inversion, composition)
  • Nesterov-Todd scaling identity verification
  • SDP cone arithmetic (xsdc!, dsdc!) and their inverse relationship
  • Line search (maxstep_sdc) correctness
  • Block operations with mixed cone types
  • Multiple SDP blocks and mixed R+Q+S cone problems
  • Edge cases (1×1 scalar, 2×2 matrices, already-PSD, zero matrix, highly non-PSD targets)
  • Cross-solver consistency (QR, sparse, 2×2 KKT solvers)

• New problem generator file test/sdp_problems.jl (420 lines): Reusable SDP problem instances:

  • sdp_psd_projection: Project matrices with mixed-sign eigenvalues onto PSD cone
  • sdp_trace_minimization: Minimize trace subject to PSD constraint
  • sdp_max_cut_relaxation: Goemans-Williamson relaxation for random graphs
  • sdp_lovasz_theta: Lovász theta number computation
  • sdp_nearest_correlation: Find nearest correlation matrix with unit diagonal
  • sdp_multiple_blocks: Multiple independent SDP blocks
  • sdp_mixed_cones: Heterogeneous R+, SOC, and SDP cones
  • sdp_with_equality: SDP with equality constraints
  • sdp_rank_one: SDP with rank-1 optimal solution
  • sdp_identity_feasible: Trivially feasible problem
  • sdp_larger: Scaling test with n=10

• New evaluation harness test/sdp_harness.jl (272 lines):

  • SDPResult struct for collecting detailed diagnostics (status, iterations, solve time, feasibility, objective error, solution error)
  • sdp_solve(): Run single problem with validation against known solutions
  • run_sdp_harness(): Batch execution across multiple problems
  • run_sdp_harness_all_solvers(): Cross-solver validation
  • print_sdp_report(): Formatted summary table with pass/fail indicators

• Integration into test suite: Added include("sdp_tests.jl") to test/runtests.jl

• Development container: Added .devcontainer/devcontainer.json for Julia 1.10 development environment

• Production plan document SDP_PRODUCTION_PLAN.md: Detailed roadmap for moving SDP from experimental to production status, covering:

  • Current state assessment
  • Five phases: correctness coverage, numerical robustness, performance, KKT solver integration, MOI wrapper completeness
  • Specific issues and recommended fixes (e.g., nestod_sdc Cholesky robustness, maxstep_sdc eigenvalue handling, VecCongurance KKT solver integration)

Notable Implementation Details

• Tests validate both correctness (solution accuracy) and numerical properties (PSD verification via eigenvalues)
• Problem generators include known optimal solutions where available for validation
• Harness supports optional equality constraints (G, d) and handles both QP and LP formulations
• Cross-solver testing ensures consistency across kktsolver_qr, kktsolver_sparse, and kktsolver_2x2
• Helper functions _vdim() and _extract_sdp_matrix() abstract away vectorization details
• All tests use configurable tolerances (optTol, tol) for robustness across

https://claude.ai/code/session_01PNGZft69CuPURr3qSAt8xe