# A Gradient-Based Implementation of the Polyhedral Active Set Algorithm

arXiv: https://arxiv.org/abs/2202.05353 · HTML: https://mlsanity.com/paper/2202.05353/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [NewVEM: A Newton Vertex Exchange Method for a Class of Constrained Self-Concordant Minimization Problems](https://mlsanity.com/paper/2407.03294/) (2024)

## Abstract (arXiv)

The Polyhedral Active Set Algorithm (PASA) is designed to optimize a general nonlinear function over a polyhedron. Phase one of the algorithm is a nonmonotone gradient projection algorithm, while phase two is an active set algorithm that explores faces of the constraint polyhedron. A gradient-based implementation is presented, where a projected version of the conjugate gradient algorithm is employed in phase two. Asymptotically, only phase two is performed. Comparisons are given with IPOPT using polyhedral constrained problems from CUTEst and the Maros/Meszaros quadratic programming test set.