# A Limited-Memory Quasi-Newton Algorithm for Bound-Constrained Nonsmooth Optimization

arXiv: https://arxiv.org/abs/1612.07350 · HTML: https://mlsanity.com/paper/1612.07350/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2016.

## Built on by (most cited first, 2 of 2)

- [Better SGD using Second-order Momentum](https://mlsanity.com/paper/2103.03265/) (2021)
- [Extending the Abstraction of Personality Types based on MBTI with Machine Learning and Natural Language Processing](https://mlsanity.com/paper/2105.11798/) (2021)

## Abstract (arXiv)

We consider the problem of minimizing a continuous function that may be nonsmooth and nonconvex, subject to bound constraints. We propose an algorithm that uses the L-BFGS quasi-Newton approximation of the problem's curvature together with a variant of the weak Wolfe line search. The key ingredient of the method is an active-set selection strategy that defines the subspace in which search directions are computed. To overcome the inherent shortsightedness of the gradient for a nonsmooth function, we propose two strategies. The first relies on an approximation of the ε-minimum norm subgradient, and the second uses an iterative corrective loop that augments the active set based on the resulting search directions. We describe a Python implementation of the proposed algorithm and present numerical results on a set of standard test problems to illustrate the efficacy of our approach.