Minimizing the Difference of Dual Functions of Two Coradiant Functions

In this article, we solve the problem of minimizing the difference of dual functions of two coradiant functions. We do this by applying a type of duality, that is used in microeconomic theory. Indeed, the dual function of a co-radiant function is decreasing and inverse coradiant. So, we first give v...

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Bibliographic Details
Published in:Numerical functional analysis and optimization 2019-02, Vol.40 (3), p.280-302
Main Authors: Mohebi, A., Mohebi, H.
Format: Article
Language:English
Subjects:
Abstract convexityl
coradiant function
DAC-function
DC-function
dual function
Economic models
global minimization
inverse co-radiant function
maximal element
subdifferential
support set
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Summary:In this article, we solve the problem of minimizing the difference of dual functions of two coradiant functions. We do this by applying a type of duality, that is used in microeconomic theory. Indeed, the dual function of a co-radiant function is decreasing and inverse coradiant. So, we first give various characterizations for the maximal elements of the support sets of this class of functions. Next, by using these results, we obtain the necessary and sufficient conditions for the global minimizers of the difference of two decreasing and inverse coradiant functions. Finally, as an application, we present the necessary and sufficient conditions for the global minimizers of the difference of dual functions of two co-radiant functions.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1553184