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On the Range of the Pseudomonotone Second-Order Cone Linear Complementarity Problem

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Abstract

In this paper, we provide a complete characterization of the range of the pseudomonotone second-order cone linear complementarity problem. In particular, by answering the three questions that under what conditions the range is the whole space, convex and closed, respectively, we explicitly characterize and formulate the range of the pseudomonotone second-order cone linear complementarity problem.

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Acknowledgements

We thank the two anonymous referees for their helpful suggestions and comments which have improved the presentation of this paper significantly. The work of Wei Hong Yang was supported by the National Natural Science Foundation of China NSFC-11371102 and NSFC Key Project 91330201. The work of Lei-Hong Zhang was supported in part by the National Natural Science Foundation of China NSFC-11371102, NSFC-11671246, and the Basic Academic Discipline Program, the 11th five year plan of 211 Project for Shanghai University of Finance and Economics. The work of Chungen Shen was supported in part by the National Natural Science Foundation of China NSFC-11271259.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Wei Hong Yang

  2. School of Mathematics, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai, 200433, People’s Republic of China

    Lei-Hong Zhang

  3. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China

    Chungen Shen

Authors
  1. Wei Hong Yang
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  2. Lei-Hong Zhang
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  3. Chungen Shen
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Correspondence to Wei Hong Yang.

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Communicated by Nobuo Yamashita.

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Yang, W.H., Zhang, LH. & Shen, C. On the Range of the Pseudomonotone Second-Order Cone Linear Complementarity Problem. J Optim Theory Appl 173, 504–522 (2017). https://doi.org/10.1007/s10957-017-1090-7

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