Online Interior Point Method

Critical analysis of the paper "Online Interior Point Methods for Time-Varying Equality Constraints" (OIPM-TEC).

GitHub: https://github.com/LORER-MTL/online-ipm

Repository Structure

• OIPM-TEC-review/ - Paper review and analysis
  • main.tex / main.pdf - LaTeX review document
  • proof_errors_analysis.md - Detailed analysis of proof errors
  • slack_variable_analysis.md - Why slack variable projection fails for inequalities
  • barrier_reformulation_analysis.md - Why barrier reformulation fails for inequalities
  • open_m_correctness_analysis.md - Analysis of OPEN-M paper correctness
• papers/ - Reference papers (MOSP.pdf, OIPM_JLL.pdf, OPEN-TEC-JLL.pdf)
• online_ipm/ - Source code and numerical experiments

Setup

# Install dependencies (uses uv package manager)
uv sync

# Alternative: traditional pip
pip install -e .

Running Experiments

# Run all numerical experiments
uv run python -m online_ipm.experiments.run_all

# Run individual experiments
uv run python -m online_ipm.experiments.test_orthonormal_basis
uv run python -m online_ipm.experiments.test_slack_projection
uv run python -m online_ipm.experiments.test_barrier_method

Building the LaTeX Document

cd OIPM-TEC-review
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex

Key Findings

OIPM-TEC Paper: Contains Critical Errors

The OIPM-TEC paper contains critical errors in its proofs (Lemmas invHess, nred, yx, and barrier complexity argument). See OIPM-TEC-review/proof_errors_analysis.md for details.

OPEN-M Paper: Correct but Misleading

The original OPEN-M paper (time-varying equality constraints) is mathematically sound but contains a misleading claim: "Without loss of generality, we let F_t = F̄_t" (orthonormal basis). Orthonormality is a required assumption, not optional—bounds inflate by κ(F_t)³ otherwise.

See OIPM-TEC-review/open_m_correctness_analysis.md for details.