Implement comprehensive duality calculations and solution storage

[napinoco]

Summary

• Implement manual duality gap, primal/dual
  infeasibility calculations using unified formulas for
  fair solver comparison
• Add solution storage system with --save-solutions
  flag for verification and analysis
• Fix corrupted SDPLIB submodule structure that was
  causing GitHub Actions failures
• Clean up all deprecated light_set references from
  codebase and documentation
• Update documentation and test files for current
  requirements structure

Key Features

• Manual Duality Calculations: Uses unified
  formulas b@y - c@x for dual gap, norm(A_eq.T @ y - c)/(1 + norm(c)) for dual infeasibility, norm(A_eq @ x - b)/(1 + norm(b)) for primal infeasibility
• Solution Storage: Save optimal solutions to
  problems/solutions/ as compressed .npz files
• Sparse Array Compatibility: Uses np.sum(c ** 2) instead of np.linalg.norm(c) for sparse array
  support
• Cone-Specific Calculations: Proper dual
  infeasibility calculations for free variables,
  non-negative variables, SOC cones, and SDP cones

Technical Changes

• Enhanced scripts/solvers/python/cvxpy_runner.py
  with manual duality calculations
• Added --save-solutions command-line flag to
  main.py
• Updated scripts/benchmark/runner.py to pass
  solution saving parameter to all solvers
• Fixed submodule configuration for DIMACS and SDPLIB
  external libraries
• Removed nested .gitmodules files and infinite
  directory structures from SDPLIB

Test plan

• Validate submodule configuration fixes GitHub
  Actions checkout errors
• Verify manual duality calculations work across
  all problem types (LP, QP, SOCP, SDP)
• Test solution storage functionality with
  --save-solutions flag
• Confirm light_set references completely removed
  from codebase
• Validate updated installation instructions and
  test commands

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Code

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• PR: Implement comprehensive duality calculations and solution storage #5 - Implement comprehensive duality calculations and solution storage
• Commit: 9b66feb07045732c1bd32668c1514dc3380e11dd
• Author: @napinoco
• Generated: 2025-06-28T17:33:42.444Z

Available Reports

• 📊 Dashboard - Main benchmark overview
• ⚡ Solver Comparison - Performance comparison
• 📋 Problem Analysis - Problem insights
• 📈 Results Matrix - Problems × Solvers matrix
• 📊 Statistical Analysis - Advanced analytics
• ⚡ Performance Profiling - Performance metrics
• 🖥️ Environment Info - System specifications

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