On the convergence rate of Newton interior-point methods in the absence of strict complementarity | Zendy

Amr El-Bakry | Zendy; R. A. Tapia | Zendy; Y. Zhang | Zendy

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On the convergence rate of Newton interior-point methods in the absence of strict complementarity

Author(s) -

Amr El-Bakry,

R. A. Tapia,

Y. Zhang

Publication year - 1996

Publication title -

computational optimization and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.028

H-Index - 78

eISSN - 1573-2894

pISSN - 0926-6003

DOI - 10.1007/bf00249644

Subject(s) - mathematics , complementarity (molecular biology) , rate of convergence , duality gap , upper and lower bounds , interior point method , complementarity theory , sequence (biology) , duality (order theory) , mathematical analysis , mathematical optimization , pure mathematics , optimization problem , nonlinear system , physics , computer science , channel (broadcasting) , genetics , quantum mechanics , biology , computer network

In the absence of strict complementarity, Monteiro and Wright [7] proved that the convergence rate for a class of Newton interior-point methods for linear complementarity problems is at best linear. They also established an upper bound of 1/4 for the -factor of the duality gap sequence when the steplengths converge to one. In the current paper, we prove that the factor of the duality gap sequence is exactly 1/4. In addition, the convergence of the Tapia indicators is also discussed.

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