Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps

J.-P. Penot and P. H. Quang
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J.-P. Penot: Université de Pau
P. H. Quang: Institute of Mathematics

Journal of Optimization Theory and Applications, 1997, vol. 92, issue 2, No 7, 343-356

Abstract: Abstract We establish connections between some concepts of generalized monotonicity for set-valued maps introduced earlier and some notions of generalized convexity. Moreover, a notion of pseudomonotonicity for set-valued maps is introduced; it is shown that, if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar.

Keywords: Quasiconvex functions; pseudoconvex functions; invex functions; quasimonotone maps; pseudomonotone maps; generalized subdifferentials (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (10)

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DOI: 10.1023/A:1022659230603

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