Abstract
We present effective procedures to calculate regular normal cones and other related objects using quantifier elimination. This method of normal cone calculations is complementary to computing Lagrangians and it works best at points where the constraint qualifications fail and extra work for other methods becomes inevitable. This method also serves as a tool to calculate the regular co-derivative for semismooth* Newton methods. We list algorithms and their demonstrations of different use cases for this approach.
| Original language | English |
|---|---|
| Article number | 102456 |
| Journal | Journal of Symbolic Computation |
| Volume | 131 |
| Early online date | 13 May 2025 |
| DOIs | |
| Publication status | E-pub ahead of print - 13 May 2025 |
Data Availability Statement
We have shared the Mathematica notebook associated with the examples of this paper on ArXiv and on second author's website. No data has been used in this research.Acknowledgements
The authors thank Josef Schicho for initiating this collaboration and for his helpful comments. The authors would also like to thank James H. Davenport and Christoph Koutschan for their comments on the manuscript. The authors would also like to thank Michael Winkler and Matus Benko for their great comments and inputs, from the optimization perspective.We thank the anonymous referees for their valuable time, and insightful and in-depth feedback, which greatly contributed to improving this work, its rigor, and presentation.
Funding
The second author would like to thank the EPSRC grant number EP/T015713/1 and the FWF grant P-34501N for partially supporting his research.
| Funders | Funder number |
|---|---|
| Engineering and Physical Sciences Research Council |
Keywords
- Co-derivatives
- Cylindrical algebraic decomposition
- Nonlinear programming
- Normal cone mapping
- Quantifier elimination
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics