Journal of Optimization Theory and Applications

, Volume 181, Issue 1, pp 216–230

# Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations

• An Wang
• Yang Cao
• Jing-Xian Chen
Article

## Abstract

In this paper, by separating the differential and the non-differential parts of the generalized absolute value equations, a class of modified Newton-type iteration methods are proposed. The modified Newton-type iteration method involves the well-known Picard iteration method as the special case. Convergence properties of the new iteration schemes are analyzed in detail. In particular, some specific sufficient conditions are presented for two special coefficient matrices. Finally, two numerical examples are given to illustrate the effectiveness of the proposed modified Newton-type iteration methods.

## Keywords

Generalized absolute value equations Newton method Convergence Differential function

## Mathematics Subject Classification

65F10 90C05 90C30

## Notes

### Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 11771225, 71401082, 71771127) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX17_1905).

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## Authors and Affiliations

• An Wang
• 1
• Yang Cao
• 2
• Jing-Xian Chen
• 3
1. 1.School of ScienceNantong UniversityNantongPeople’s Republic of China
2. 2.School of TransportationNantong UniversityNantongPeople’s Republic of China
3. 3.School of BusinessNantong UniversityNantongPeople’s Republic of China