Improved convergence analysis of a smoothing Newton method for the circular cone programming

In this paper, we propose a new smoothing Newton method to solve the circular cone programming (denoted by CCP). The proposed method is designed based on a non-monotone derivative-free line search scheme. We show that any accumulation point of the iteration sequence generated by this method is a sol...

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Bibliographic Details
Published in:Optimization 2022-07, Vol.71 (7), p.2005-2031
Main Authors: Tang, Jingyong, Zhou, Jinchuan
Format: Article
Language:English
Subjects:
Accumulation
Circular cone programming
Circular cones
Convergence
derivative-free line search
Iterative methods
Newton methods
quadratical convergence
Smoothing
smoothing Newton method
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Summary:In this paper, we propose a new smoothing Newton method to solve the circular cone programming (denoted by CCP). The proposed method is designed based on a non-monotone derivative-free line search scheme. We show that any accumulation point of the iteration sequence generated by this method is a solution of the CCP. Moreover, we prove that the proposed method is locally quadratically convergent without requiring strict complementarity conditions. Compared with existing smoothing Newton methods for solving the CCP, our method has three new features: (i) the generated iteration sequence is bounded; (ii) the value of the merit function converges to zero; (iii) the whole iteration sequence converges to an accumulation point if this point is isolated. Some numerical results are reported.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1847108