A Gradient-Based Implementation of the Polyhedral Active Set Algorithm

TL;DR

This paper presents a gradient-based implementation of the Polyhedral Active Set Algorithm (PASA) for nonlinear optimization over polyhedra, combining gradient projection and active set methods, with empirical comparisons to IPOPT.

Contribution

It introduces a projected conjugate gradient approach within PASA, enhancing efficiency and asymptotic performance over existing implementations.

Findings

The gradient-based PASA outperforms IPOPT on certain test problems.

Asymptotically, only phase two of PASA is needed.

The method effectively handles polyhedral constraints.

Abstract

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.