A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization
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After a brief introduction to Jordan algebras, we present a primal–dual interior-point algorithm for second-order conic optimization that uses full Nesterov–Todd steps; no line searches are required. The number of iterations of the algorithm coincides with the currently best iteration bound for second-order conic optimization. We also generalize an infeasible interior-point method for linear optimization to second-order conic optimization. As usual for infeasible interior-point methods, the starting point depends on a positive number. The algorithm either finds a solution in a finite number of iterations or determines that the primal–dual problem pair has no optimal solution with vanishing duality gap.
KeywordsFeasible interior-point method Infeasible interior-point method Second-order conic optimization Jordan algebra Polynomial complexity
Authors wish to thank Professor Florian Potra and four anonymous referees for useful comments and suggestions on an earlier draft of the manuscript. The first author would like to thank for the financial grant from Shahrekord University. The first author was also partially supported by the Center of Excellence for Mathematics, University of Shahrekord, Shahrekord, Iran.
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