Pseudomonotonicity of a Linear Map on the Interior of the Positive Orthant

Alberto Cambini () and Laura Martein ()
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Alberto Cambini: University of Pisa
Laura Martein: University of Pisa

A chapter in Generalized Convexity and Related Topics, 2007, pp 115-131 from Springer

Abstract: Summary In this paper we will establish some necessary and/or sufficient conditions for both a nonsingular and a singular matrix A (interpreted as a linear map) to be pseudomonotone. The given results are in terms of the sign of the determinants of the principal submatrices and of the cofactors of A in the nonsingular case and in terms of the structure of A in the singular case. A complete characterization of pseudomonotonicity in terms of the coefficients of a 3 × 3 matrix is given and a method for constructing a merely pseudomonotone matrix is suggested.

Keywords: Pseudomonotonicity; pseudoconvexity; principal submatrices; cofactors; linear map (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-540-37007-9_6

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DOI: 10.1007/978-3-540-37007-9_6

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