A self-regular Newton based algorithm for linear optimization

Maziar Salahi

Abstract


In this paper, using the framework of self-regularity, we propose a hybrid adaptive algorithm for the linear optimization problem.
If the current iterate is far from central path,
it employs a self-regular search direction, otherwise the classical Newton search direction is employed. This feature of the algorithm allows us to prove a worst case iteration bound. Our result matches the best iteration bound obtained by the pure self-regular approach and improves on the worst case iteration bound of the classical algorithm.

doi:10.1017/S1446181109000340

Keywords


linear optimization, interior point methods, self-regular functions, polynomial complexity.



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.1517



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.