{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T19:36:17Z","timestamp":1754163377542,"version":"3.41.2"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p> In this paper, we revisit Scarf\u2019s 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\u201390]. We prove that the problem has a unique solution if the underlying matrix is a vertical block [Formula: see text]-matrix. Some results on the error bounds for the vertical block [Formula: see text]- and [Formula: see text]-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\u2013136] and [Mangasarian, OL and J Ren (1994). New improved error bounds for the linear complementarity problem. Mathematical Programming, 66, 241\u2013255]. <\/jats:p>","DOI":"10.1142\/s0217595924500271","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T11:43:02Z","timestamp":1728646982000},"source":"Crossref","is-referenced-by-count":0,"title":["More on Scarf\u2019s Complementarity Problem and its Error Bounds"],"prefix":"10.1142","volume":"42","author":[{"given":"S. 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