# NonOpt

Nonsmooth Optimization Solver (NonOpt) is a software package for minimizing nonsmooth functions. It is designed to locate a minimizer 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++. The code is currently under development. We are looking for test problems! If you have nonsmooth (preferably nonconvex) test problems, please let us know. We would be very interested in testing (and tuning) NonOpt with them.

NonOpt Developers
Frank E. Curtis Andreas Wächter

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

• [Download PDF] F. E. Curtis, D. P. Robinson, and B. Zhou. Self-Correcting Variable-Metric Algorithms for Nonsmooth Optimization. Technical Report 17T-012, COR@L Laboratory, Department of ISE, Lehigh University, 2017. [Bibtex]
@techreport{CurtRobiZhou17,
author = {Curtis, F. E. and Robinson, D. P. and Zhou, B.},
title = {{Self-Correcting Variable-Metric Algorithms for Nonsmooth Optimization}},
institution = {COR@L Laboratory, Department of ISE, Lehigh University},
number = {17T-012},
year = {2017},
url = {http://coral.ise.lehigh.edu/frankecurtis/files/papers/CurtRobiZhou17.pdf}
}
• [Download PDF] F. E. Curtis and X. 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 = {Curtis, F. E. and Que, X.},
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}
}
• [Download PDF] F. E. Curtis and X. Que. An Adaptive Gradient Sampling Algorithm for Nonsmooth Optimization. Optimization Methods and Software, 28(6):1302–1324, 2013. [Bibtex]
@article{CurtQue13,
author = {Curtis, F. E. and Que, X.},
}