New parameterized kernel functions for linear optimization

Authors:
Yanqin Bai;Wei Xie;Jing Zhang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China 200444;Department of Mathematics, Shanghai University, Shanghai, China 200444;Department of Mathematics, Shanghai University, Shanghai, China 200444
Venue:
Journal of Global Optimization
Year:
2012

Citing 4
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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.