Characterizing Approximate Global Minimizers of the Difference of two Abstract Convex Functions with Applications

Alireza Sattarzadeh, Hossein Mohebi


In this paper, we first investigate characterizations of maximal elements
of abstract convex functions under a mild condition. Also, we give various characterizations for
global $\e$-minimum of the difference of two abstract convex functions and, by using the abstract Rockafellar's
antiderivative, we present the abstract $\e$-subdifferential of abstract convex functions
in terms of their abstract subdifferential. Finally, as an application, a necessary and sufficient condition for global $\e$-minimum of the difference of two increasing and positively homogeneous (IPH) functions is presented.


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