New Complexity Analysis of Full Nesterov-Todd Step Infeasible Interior Point Method for Second-Order Cone Optimization
Yugoslav journal of operations research, Tome 28 (2018) no. 1.

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We present a full Nesterov-Todd (NT) step infeasible interior-point algorithm for second-order cone optimization based on a different way to calculate feasibility direction. In each iteration of the algorithm we use the largest possible barrier parameter value $\theta$. Moreover, each main iteration of the algorithm consists of a feasibility step and a few centering steps. The feasibility step differs from the feasibility step of the other existing methods. We derive the complexity bound which coincides with the best known bound for infeasible interior point methods.
Mots-clés : Second-order Cone Optimization, Infeasible Interior-point Method, Full Nesterov-Todd Atep, Polynomial Complexity 
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     author = {Behrouz Kheirfam},
     title = {New {Complexity} {Analysis} of {Full} {Nesterov-Todd} {Step} {Infeasible} {Interior} {Point} {Method} for {Second-Order} {Cone} {Optimization}},
     journal = {Yugoslav journal of operations research},
     pages = {21 - 38},
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Behrouz Kheirfam. New Complexity Analysis of Full Nesterov-Todd Step Infeasible Interior Point Method for Second-Order Cone Optimization. Yugoslav journal of operations research, Tome 28 (2018) no. 1. https://geodesic-test.mathdoc.fr/item/YJOR_2018_28_1_a1/