---
license: apache-2.0
pretty_name: QP-Benchmark
tags:
- quadratic-programming
- optimization
- radiotherapy
- benchmark
---

# QP-Benchmark

Benchmark instances for **[Warm-IP](https://github.com/Radiotherapy-Optimization/Warm-IP)**,
an open-source solver for large-scale convex quadratic programs (QPs),
from the paper *Warm-IP: A Path-Following ADMM Warm Start for
Interior-Point Quadratic Programming* (Aslani, Tefagh, Jhanwar,
Zarepisheh; preprint link to be added). Every instance is a convex QP

    minimize    0.5 x'Qx + q'x + c
    subject to  constraints (one-sided or two-sided; see below)

stored as an HDF5 (`.h5`) file, one folder per family:

    MPC_data/        64 model-predictive-control instances  MPC_001_....h5
    MM_data/        137 Maros-Meszaros instances            MM_001_....h5
    IMRT_lung_data/  60 radiotherapy (lung IMRT) instances  IMRT_lung_001.h5

Radiotherapy data is organized one folder per (modality, site) family --
`IMRT_lung` today; future releases may add sibling families such as
`IMRT_prostate` or `VMAT_lung` -- and radiotherapy instance names are
exactly `<family>_<index>`. Everything else about an instance (patient,
treatment protocol, provenance) lives in the manifest
(`instances_metadata.csv`, one row per instance: family, name, source,
sizes, nonzero counts, protocol, the spelled-out problem formulation,
note) and in each file's `data_note`, never in folder or file names.

## Using the data

The [Warm-IP repository](https://github.com/Radiotherapy-Optimization/Warm-IP)
downloads these files automatically (its `src/data_loader.py` fetches
any requested instance on first use), so nothing needs to be downloaded
by hand. To fetch files directly:

```python
from huggingface_hub import hf_hub_download
path = hf_hub_download(
    repo_id="Radiotherapy-Optimization/QP-Benchmark", repo_type="dataset",
    filename="IMRT_lung_data/IMRT_lung_001.h5")
```

## File format

`Q` (n x n, full symmetric) and the constraint matrix `G` (m x n) are
stored in CSR form as four datasets each (`Q_data`, `Q_indices`,
`Q_indptr`, `Q_shape`, and likewise for `G`); `q` and `c` are stored
directly. Two constraint forms are used:

* **Canonical (radiotherapy files)** -- dataset `h` is present:
  `G x <= h`.
* **Two-sided (MM and MPC files)** -- datasets `l_h`, `u_h`, `l_x`,
  `u_x` are present: `l_h <= G x <= u_h`, `l_x <= x <= u_x`, with
  infinite entries encoding absent bounds; a row with `l_h[i] == u_h[i]`
  is an equality constraint.

Every file carries `format_note` (format description) and `data_note`
(provenance). See the
[data documentation](https://github.com/Radiotherapy-Optimization/Warm-IP/blob/main/data/README.md)
in the Warm-IP repository for full details, family descriptions, and
references.

## Sources

* **MPC**: the qpbenchmark MPC test set (Caron et al., 2024),
  [qpsolvers/mpc_qpbenchmark](https://github.com/qpsolvers/mpc_qpbenchmark).
* **MM**: the Maros-Meszaros convex QP test set (Maros and Meszaros,
  1999), via
  [qpsolvers/maros_meszaros_qpbenchmark](https://github.com/qpsolvers/maros_meszaros_qpbenchmark).
* **IMRT_lung**: fluence-map-optimization QPs built from the public
  lung-patient data of
  [PortPy](https://github.com/PortPy-Project/PortPy) (Jhanwar et al.,
  2023), one instance per patient under the `Lung_2Gy_30Fx` protocol.

## Citing

If you use this data, please cite the Warm-IP paper (BibTeX in the
[repository README](https://github.com/Radiotherapy-Optimization/Warm-IP#citing))
and the original sources above for the family you use.