In the recent literature, the connection between maximal monotone operators and the Fitzpatrick function is investigated. Subsequently, this relation has been extended to maximal monotone bifunctions and their Fitzpatrick transform. In this paper we generalize some of these results to maximal n-cyclically monotone and maximal cyclically monotone bifunctions, by introducing and studying the Fitzpatrick transforms of order n or infinite order for bifunctions.
Bianchi, M., Hadjisavvas, N., Pini, R., Alizadeh, M. H., On cyclic and n-cyclic monotonicity of bifunctions, <<JOURNAL OF GLOBAL OPTIMIZATION>>, 2014; 2014 (60): 599-616. [doi:10.1007/s10898-013-0113-7] [http://hdl.handle.net/10807/61598]
On cyclic and n-cyclic monotonicity of bifunctions
Bianchi, Monica;
2014
Abstract
In the recent literature, the connection between maximal monotone operators and the Fitzpatrick function is investigated. Subsequently, this relation has been extended to maximal monotone bifunctions and their Fitzpatrick transform. In this paper we generalize some of these results to maximal n-cyclically monotone and maximal cyclically monotone bifunctions, by introducing and studying the Fitzpatrick transforms of order n or infinite order for bifunctions.
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