# New parameterized kernel functions for linear optimization

Listed:
• Yanqin Bai

()

• Wei Xie
• Jing Zhang

## Abstract

Recent studies on the kernel function-based primal-dual interior-point algorithms indicate that a kernel function not only represents a measure of the distance between the iteration and the central path, but also plays a critical role in improving the computational complexity of an interior-point algorithm. In this paper, we propose a new class of parameterized kernel functions for the development of primal-dual interior-point algorithms for solving linear programming problems. The properties of the proposed kernel functions and corresponding parameters are investigated. The results lead to a complexity bounds of $${O\left(\sqrt{n}\,{\rm log}\,n\,{\rm log}\,\frac{n}{\epsilon}\right)}$$ for the large-update primal-dual interior point methods. To the best of our knowledge, this is the best known bound achieved. Copyright Springer Science+Business Media, LLC. 2012

## Suggested Citation

• Yanqin Bai & Wei Xie & Jing Zhang, 2012. "New parameterized kernel functions for linear optimization," Journal of Global Optimization, Springer, vol. 54(2), pages 353-366, October.
• Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:353-366
DOI: 10.1007/s10898-012-9934-z
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File URL: http://hdl.handle.net/10.1007/s10898-012-9934-z

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## References listed on IDEAS

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1. Alexandru Kristály & Waclaw Marzantowicz & Csaba Varga, 2010. "A non-smooth three critical points theorem with applications in differential inclusions," Journal of Global Optimization, Springer, vol. 46(1), pages 49-62, January.
2. Kaimin Teng, 2010. "Multiple solutions for semilinear resonant elliptic problems with discontinuous nonlinearities via nonsmooth double linking theorem," Journal of Global Optimization, Springer, vol. 46(1), pages 89-110, January.
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### Keywords

Linear programming; Primal-dual interior-point method; Large-update methods; 60K05; 90C51;

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