More on Scarf’s Complementarity Problem and its Error Bounds

S. K. Neogy (), A. Gupta () and P. Mondal
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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

Asia-Pacific Journal of Operational Research (APJOR), 2025, vol. 42, issue 04, 1-14

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].

Keywords: Linear complementarity problem; global error bound; scarf’s linear complementarity problem; R0-matrix; vertical block R0-matrix (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0217595924500271

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