IGAOS — Indigenous GPU-Accelerated Optimization Solver

A sovereign LP / MILP / QP solver core built from mathematical foundations for SIH 2026 problem statement SIH26119 (MRPL): revised simplex (primal + dual), first-order GPU methods (PDHG), branch-and-bound with Gomory cuts, and ADMM QP — no existing optimization-solver library as a base.

• Wayfinder map: issue #1
• Problem-statement analysis: docs/SIH26119-RESEARCH-REPORT.md
• Research sheets: docs/research/ (PDHG algorithm · simplex design · benchmark protocol · refinery cases)
• Dependency policy: docs/DEPENDENCIES.md · vocabulary: CONTEXT.md

Layout

src/
  common/   shared types, numerics utilities
  linalg/   sparse/dense linear algebra; swappable CPU/GPU backends
  simplex/  revised simplex (primal + dual, eta updates, warm starts)
  pdhg/     first-order GPU LP engine
  milp/     branch-and-bound + Gomory cuts
  qp/       OSQP-style ADMM QP engine
  io/       MPS reader (LP/MILP/QP), solution writers
  api/      CLI + pybind11 surface
python/     Python bindings: igaos.solve() / igaos.read_mps()
benchmarks/ harness per docs/research/benchmark-protocol.md
tests/      assert-based engine smoke tests

Install

Python package (CPU engines — simplex LP, MILP, QP):

pip install igaos

import igaos
sol = igaos.solve("model.mps", time_limit=60, engine="auto")
sol.status, sol.objective, sol.x

With the GPU PDHG engine, build from source on a machine with the CUDA toolkit (auto-detected when nvcc is present):

pip install igaos --no-binary igaos --config-settings=cmake.define.IGAOS_ENABLE_CUDA=ON

Build from source (CLI + tests)

cmake -S . -B build
cmake --build build

Builds CPU-only automatically when no CUDA toolchain is present (the PDHG engine requires CUDA). The CLI binary is build/src/api/igaos; the Python module lands in python/igaos/. Engine tests: ctest --test-dir build.

Solve

$ ./build/src/api/igaos solve model.mps --engine auto --time-limit 60
{
  "instance": "model.mps",
  "status": "optimal",
  "objective": -464.7531429,
  ...
}

Engines: auto | simplex | pdhg | milp | qp. All four engine classes are live and verified against pinned baselines — current scores: Netlib 52/64 exact vs HiGHS, MIPLIB starters 6/20 @1e-4, robustness suite 10/15 per-class gates, Haverly QP three-way verified. Details and honest failure records: docs/research/.

Python:

import igaos
sol = igaos.solve("model.mps", time_limit=60, engine="milp")
sol.status, sol.objective, sol.x