A Newton-Type Active Set Method for Nonlinear Optimization with Polyhedral Constraints
Abstract
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix, and a set of rules for branching between the two steps. We show that the proposed method asymptotically takes the Newton step when the active constraints are linearly independent and a strong second-order sufficient optimality condition holds. We also show that the method has a quadratic rate of convergence under standard conditions. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEst and on a specific class of problems for which finding second-order stationary points is critical.
Cite
@article{arxiv.2011.01201,
title = {A Newton-Type Active Set Method for Nonlinear Optimization with Polyhedral Constraints},
author = {William W. Hager and Davoud Ataee Tarzanagh},
journal= {arXiv preprint arXiv:2011.01201},
year = {2021}
}