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Generalizations of $$R_0$$ R 0 and $$\textbf{SSM}$$ SSM Properties for Extended Horizontal Linear Complementarity Problem

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  • Punit Kumar Yadav

    (Malaviya National Instiute of Technology Jaipur)

  • Palpandi Karuppaiah

    (Malaviya National Instiute of Technology Jaipur)

Abstract

In the setting of the Extended Horizontal Linear Complementarity Problem, we study boundedness, nonemptyness, uniqueness and connectedness issues of solution sets. We introduce column $$R_0$$ R 0 -W and column $$\textbf{SSM}$$ SSM -W properties and, using degree theory, establish boundedness and existence results. Some uniqueness results are also covered. We provide a necessary condition and a sufficient condition for EHLCP to have connected solution sets.

Suggested Citation

  • Punit Kumar Yadav & Palpandi Karuppaiah, 2023. "Generalizations of $$R_0$$ R 0 and $$\textbf{SSM}$$ SSM Properties for Extended Horizontal Linear Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 392-414, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02262-9
    DOI: 10.1007/s10957-023-02262-9
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    References listed on IDEAS

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    1. Francesco Mezzadri & Emanuele Galligani, 2019. "Splitting Methods for a Class of Horizontal Linear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 500-517, February.
    2. Xiaoni Chi & M. Seetharama Gowda & Jiyuan Tao, 2019. "The weighted horizontal linear complementarity problem on a Euclidean Jordan algebra," Journal of Global Optimization, Springer, vol. 73(1), pages 153-169, January.
    3. M. Seetharama Gowda, 1993. "Applications of Degree Theory to Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 868-879, November.
    4. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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