Optimization of the difference of topical functions
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In this paper, we first obtain some properties of topical (increasing and plus-homogeneous) functions in the framework of abstract convexity. Next, we use the Toland–Singer formula to characterize the dual problem for the difference of two topical functions. Finally, we present necessary and sufficient conditions for the global minimum of the difference of two strictly topical functions.
KeywordsGlobal optimization Monotonic analysis Abstract convexity Topical function Toland–Singer formula Support set Subdifferential set
Mathematics Subject Classification (2000)90C46 26A48
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