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Abstract
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In this paper, based on the transformation ψ( xs
µ ) = ψ(qxs
µ ) introduced by Darvay and
Tak´acs [New method for determining search directions for interior-point algorithms in
linear optimization, Optim. Lett. 12(5) (2018) 1099–1116], we present a full-Newton step
interior-point method for linear optimization. They consider the case ψ(t) = t2. Here, we
extend this to the case ψ(t) = tq(q ≥ 2) to obtain our search directions. We show that
the iterates lie in the neighborhood of the local quadratic convergence of the proximity
measure. Finally, the polynomial complexity of the proposed algorithm is proved.
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