# NonOpt

NonOpt (Nonlinear/nonconvex/nonsmooth Optimizer) is a software package for minimization. It is designed to locate a minimizer (or at least a stationary point) of

$$\min_{x\in\mathbb{R}^n}\ \ f(x)$$

where $$f : \mathbb{R}^n \to \mathbb{R}$$ is locally Lipschitz and continuously differentiable over a full-measure subset of $$\mathbb{R}^n$$. The function $$f$$ is allowed to be nonconvex.

NonOpt is written in C++. It is available at the NonOpt page on GitHub.

We are looking for test problems! If you have nonlinear/nonsmooth/nonconvex test problems, please let us know. We would be very interested in testing (and tuning) NonOpt with them.

## Citing NonOpt

NonOpt is based on the algorithms described in the following papers.

• [Download PDF] Frank E. Curtis, Daniel P. Robinson, and Baoyu Zhou. A Self-Correcting Variable-Metric Algorithm Framework for Nonsmooth Optimization. IMA Journal of Numerical Analysis, 40(2):1154–1187, 2020. [Bibtex]
@article{CurtRobiZhou20,
author = {Frank E. Curtis and Daniel P. Robinson and Baoyu Zhou},
title = {{A Self-Correcting Variable-Metric Algorithm Framework for Nonsmooth Optimization}},
journal = {{IMA Journal of Numerical Analysis}},
volume = {40},
number = {2},
pages = {1154--1187},
year = {2020},
papercite = {3. Journal Articles}
}
• [Download PDF] Frank E. Curtis and Xiaocun Que. A Quasi-Newton Algorithm for Nonconvex, Nonsmooth Optimization with Global Convergence Guarantees. Mathematical Programming Computation, 7(4):399–428, 2015. [Bibtex]
@article{CurtQue15,
author = {Frank E. Curtis and Xiaocun Que},
title = {{A Quasi-Newton Algorithm for Nonconvex, Nonsmooth Optimization with Global Convergence Guarantees}},
journal = {{Mathematical Programming Computation}},
volume = {7},
number = {4},
pages = {399--428},
year = {2015},
url = {http://coral.ise.lehigh.edu/frankecurtis/files/papers/CurtQue15.pdf},
papercite = {3. Journal Articles}
}
• [Download PDF] Frank E. Curtis and Xiaocun Que. An Adaptive Gradient Sampling Algorithm for Nonsmooth Optimization. Optimization Methods and Software, 28(6):1302–1324, 2013. [Bibtex]
@article{CurtQue13,
author = {Frank E. Curtis and Xiaocun Que},
}