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Solving system of inequalities via a smoothing homotopy method

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Abstract

In this paper, the system of nonlinear inequalities is considered. The problem is approximated by the parameterized smooth equations which is formed by Chen-Harker-Kanzow-Smale smoothing function. A smoothing homotopy method is proposed to solve the system of smooth equations. For almost all initial points in Euclidean space, the existence and convergence of the homotopy path is proved under certain weaker condition without assumption of the monotonicity. The numerical results illustrate that the method is effective.

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Acknowledgments

The authors are grateful to the anonymous referee for the suggestions which improved the paper. The work is supported by Foundation of NJUPT under Grant Nos. NY217097, NY218061, NY218079 and the Natural Science Foundation of China under Grant Nos. 11671004, 11201240.

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Authors and Affiliations

  1. School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210023, People’s Republic of China

    Xiaona Fan & Qinglun Yan

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  1. Xiaona Fan
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  2. Qinglun Yan
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Correspondence to Xiaona Fan.

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Fan, X., Yan, Q. Solving system of inequalities via a smoothing homotopy method. Numer Algor 82, 719–728 (2019). https://doi.org/10.1007/s11075-018-0622-z

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  • DOI: https://doi.org/10.1007/s11075-018-0622-z

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Mathematics Subject Classification (2010)