Article ID: | iaor20124134 |
Volume: | 53 |
Issue: | 2 |
Start Page Number: | 137 |
End Page Number: | 163 |
Publication Date: | Jun 2012 |
Journal: | Journal of Global Optimization |
Authors: | Mohebi H, Martnez-Legaz J -E, Rocco M |
Keywords: | duality, monotonicity |
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.