EURO Journal on Computational Optimization

, Volume 3, Issue 4, pp 309–348

# An interior-point method for nonlinear optimization problems with locatable and separable nonsmoothness

Original Paper

## Abstract

Many real-world optimization models comprise nonconvex and nonsmooth functions leading to very hard classes of optimization models. In this article, a new interior-point method for the special, but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under consideration, modifications and extensions to a standard interior-point method for nonlinear programming are investigated to solve the introduced problem class. First theoretical results are given and a numerical study is presented that shows the applicability of the new method for real-world instances from gas network optimization.

### Keywords

Interior-point methods Barrier methods Line-search methods Nonlinear and nonsmooth optimization Classification of optimization models  Gas network optimization

### Mathematics Subject Classification

90C30 90C51 90C90 90C35 90C56 90B10

## Notes

### Acknowledgments

This work has been supported by the German Federal Ministry of Economics and Technology owing to a decision of the German Bundestag. The responsibility for the content of this publication lies with the author. The author would also like to thank Open Grid Europe GmbH and the project partners in the ForNe consortium. This research was performed as part of the Energie Campus Nürnberg and supported by funding through the “Aufbruch Bayern (Bavaria on the move)” initiative of the state of Bavaria. Moreover, the author thanks Marc C. Steinbach, Jan Thiedau, and Andreas Wächter for several comments on the algorithm. At last, the author is also very grateful to three anonymous referees, whose comments greatly helped to improve the quality of the paper.

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