Two wide neighborhood interior-point methods for symmetric cone optimization

Two wide neighborhood interior-point methods for symmetric cone optimization

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Article ID: iaor20173358
Volume: 68
Issue: 1
Start Page Number: 29
End Page Number: 55
Publication Date: Sep 2017
Journal: Computational Optimization and Applications
Authors: , ,
Keywords: heuristics
Abstract:

In this paper, we present two primal–dual interior‐point algorithms for symmetric cone optimization problems. The algorithms produce a sequence of iterates in the wide neighborhood N ( τ , β ) equ1 of the central path. The convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the xs and sx directions. We derive that these two path‐following algorithms have O r cond ( G ) log ϵ 1 , O r cond ( G ) 1 / 4 log ϵ 1 equ2 iteration complexity bounds, respectively. The obtained complexity bounds are the best result in regard to the iteration complexity bound in the context of the path‐following methods for symmetric cone optimization. Numerical results show that the algorithms are efficient for this kind of problems.

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