A Log-Barrier Newton-CG Method for Bound Constrained Optimization with Complexity Guarantees
Optimization and Control
2019-12-05 v2
Abstract
We describe an algorithm based on a logarithmic barrier function, Newton's method, and linear conjugate gradients that obtains an approximate minimizer of a smooth function over the nonnegative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.
Cite
@article{arxiv.1904.03563,
title = {A Log-Barrier Newton-CG Method for Bound Constrained Optimization with Complexity Guarantees},
author = {Michael O'Neill and Stephen J. Wright},
journal= {arXiv preprint arXiv:1904.03563},
year = {2019}
}