A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization

M. Zangiabadi (), G. Gu () and C. Roos ()
Additional contact information
M. Zangiabadi: Shahrekord University
G. Gu: Nanjing University
C. Roos: Delft University of Technology

Journal of Optimization Theory and Applications, 2013, vol. 158, issue 3, No 10, 816-858

Abstract: Abstract 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.

Keywords: Feasible interior-point method; Infeasible interior-point method; Second-order conic optimization; Jordan algebra; Polynomial complexity (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-013-0278-8

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