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More on Scarf’s Complementarity Problem and its Error Bounds

Author

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  • S. K. Neogy

    (Indian Statistical Institute, Delhi Center, New Delhi 110016, India)

  • A. Gupta

    (Indian Statistical Institute, Kolkata Center, Kolkata 700108, India)

  • P. Mondal

    (Mathematics Department, Government General Degree College at Ranibandh, Bankura 722135, India)

Abstract

In this paper, we revisit Scarf’s complementarity problem involving a rectangular matrix, known as the vertical block matrix introduced by [Cottle, RW and GB Dantzig (1970). A generalization of the linear complementarity problem. Journal of Combinatorial Theory, 8, 79–90]. We prove that the problem has a unique solution if the underlying matrix is a vertical block P-matrix. Some results on the error bounds for the vertical block P- and R0-matrices are derived. This further extends the results on global error bounds obtained by [Mathias, R and JS Pang (1990). Error bounds for the linear complementarity problem with a P-matrix. Linear Algebra and its Applications, 132, 123–136] and [Mangasarian, OL and J Ren (1994). New improved error bounds for the linear complementarity problem. Mathematical Programming, 66, 241–255].

Suggested Citation

  • S. K. Neogy & A. Gupta & P. Mondal, 2025. "More on Scarf’s Complementarity Problem and its Error Bounds," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 42(04), pages 1-14, August.
    • Handle: RePEc:wsi:apjorx:v:42:y:2025:i:04:n:s0217595924500271
    DOI: 10.1142/S0217595924500271
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