Self-regular functions and new search directions for linear and semidefinite optimization

@article{Peng2002SelfregularFA,
  title={Self-regular functions and new search directions for linear and semidefinite optimization},
  author={Jiming Peng and Kees Roos and Tam{\'a}s Terlaky},
  journal={Mathematical Programming},
  year={2002},
  volume={93},
  pages={129-171}
}
Abstract.In this paper, we introduce the notion of a self-regular function. Such a function is strongly convex and smooth coercive on its domain, the positive real axis. We show that any such function induces a so-called self-regular proximity function and a corresponding search direction for primal-dual path-following interior-point methods (IPMs) for solving linear optimization (LO) problems. It is proved that the new large-update IPMs enjoy a polynomial ?(n$\frac{q+1}{2q}$log$\frac{n… Expand
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