Abstract
New concepts of strong pseudomonotonicity, strict quasimonotonicity, and semistrict quasimonotonicity of a map are introduced and their properties are studied. In the case of a differentiable gradient map, we show that strong pseudomonotonicity of the gradient is equivalent to strong pseudoconvexity of the underlying function. This does not hold for a different concept of strong pseudomonotonicity in Ref. 1. Analogous results are shown for strict quasimonotonicity and semistrict quasimonotonicity.
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Hadjisavvas, N., Schaible, S. On strong pseudomonotonicity and (semi)strict quasimonotonicity. J Optim Theory Appl 79, 139–155 (1993). https://doi.org/10.1007/BF00941891
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DOI: https://doi.org/10.1007/BF00941891