Journal of Global Optimization

, Volume 53, Issue 2, pp 137–163

Some criteria for maximal abstract monotonicity

Article

DOI: 10.1007/s10898-011-9671-8

Cite this article as:
Mohebi, H., Martínez-Legaz, JE. & Rocco, M. J Glob Optim (2012) 53: 137. doi:10.1007/s10898-011-9671-8

Abstract

In this paper, we develop a theory of monotone operators in the framework of abstract convexity. First, we provide a surjectivity result for a broad class of abstract monotone operators. Then, by using an additivity constraint qualification, we prove a generalization of Fenchel’s duality theorem in the framework of abstract convexity and give some criteria for maximal abstract monotonicity. Finally, we present necessary and sufficient conditions for maximality of abstract monotone operators.

Keywords

Constraint qualification Generalized Fenchel’s duality Monotone operator Abstract monotonicity Abstract convex function Abstract convexity 

Mathematics Subject Classification (2000)

47H05 47H04 52A01 26A51 26B25 

Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of MathematicsShahid Bahonar University of KermanKermanIran
  2. 2.School of Mathematical and Geospatial SciencesRMIT UniversityMelbourneAustralia
  3. 3.Departament d’Economia i d’Història EconòmicaUniversitat Autònoma de BarcelonaBellaterraSpain
  4. 4.Department of Mathematics, Statistics, Computer Science and ApplicationsUniversity of BergamoBergamoItaly

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