A polynomial-time algorithm for linear optimization based on a new class of kernel functions
Journal of Computational and Applied Mathematics
ISNN 2009 Proceedings of the 6th International Symposium on Neural Networks: Advances in Neural Networks - Part III
Polynomial interior-point algorithms for P*(K) horizontal linear complementarity problem
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
New parameterized kernel functions for linear optimization
Journal of Global Optimization
Journal of Computational and Applied Mathematics
Interior-point algorithms for $$P_{*}(\kappa )$$-LCP based on a new class of kernel functions
Journal of Global Optimization
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We introduce a new barrier-type function which is not a barrier function in the usual sense: it has finite value at the boundary of the feasible region. Despite this, the iteration bound of a large-update interior-point method based on this function is shown to be $O({\sqrt{n}\,({\rm log}\,n)\,{\rm log}\,\frac{n}{\varepsilon}})$, which is as good as the currently best known bound for large-update methods. The recently introduced property of \emph{exponential convexity} for the kernel function underlying the barrier function, as well as the strong convexity of the kernel function, are crucial in the analysis.