Abstract
In this paper, we extend the concept of pseudomonotonicity from Rn to the setting of Euclidean Jordan algebras. We study interconnections between pseudomonotonicity, monotonicity, and the Z-property. Motivated by their results, in this paper, we extend the concept of pseudomono- tonicity from R n to the setting of Euclidean Jordan algebras. Specifically, we give a characterization of pseudomonotonicity for a linear transformation and a matrix- induced transformation defined on a Euclidean Jordan algebra. We show that pseu- domonotonicity and monotonicity coincide under the condition of the Z-property. Moreover, we present the invariance of pseudomonotonicity under the algebra and cone automorphisms and describe interconnections between pseudomonotonicity of a linear transformation and its principal subtransformations. We note that symmetric cones (see Section 2 for definition) are, in general, nonpolyhedral. Therefore, these generalizations presented in this paper are not routine generalizations.
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