Papers by Ali Moslemipour
Optimization, Apr 17, 2024
arXiv (Cornell University), Jun 21, 2021
In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are inve... more In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element p in an Hadamard space X, the notion of p-Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved. Moreover, we examine the p-Fitzpatrick transform and its main properties for monotone set-valued operators in Hadamard spaces. Furthermore, some relations between maximal monotone operators and certain classes of proper, convex, l.s.c. extended real-valued functions on X × X ♦ , are given.
In this paper, the notion of W-property for subsets of X× X^ is introduced and investigated, wher... more In this paper, the notion of W-property for subsets of X× X^ is introduced and investigated, where X is an Hadamard space and X^ is its linear dual space. It is shown that an Hadamard space X is flat if and only if X× X^ has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is proved.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2020
In the present paper, monotone relations and maximal monotone relations from an Hadamard space to... more In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.
In this paper, the notion ofW-property for subsets of X × X is introduced and investigated, where... more In this paper, the notion ofW-property for subsets of X × X is introduced and investigated, where X is an Hadamard space and X is its linear dual space. It is shown that an Hadamard space X is flat if and only if X × X hasW-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. Finally, a characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is proved.
This paper is devoted to study some topics of monotone operator theory in the context of Hadamard... more This paper is devoted to study some topics of monotone operator theory in the context of Hadamard spaces. For a fixed element p in an Hadamard space X, the notion of p-Fenchel conjugate is introduced and a generalization of Fenchel-Young inequality is proved. Moreover, p-Fitzpatrick transform of a monotone set-valued operator from an Hadamard space X to its linear dual space X ◊ and its main properties are investigated. Finally, a characterization result for maximality of monotone operator T ∶ X ⊸ X ◊ , based on certain classes of proper, convex, l.s.c. extended real-valued function h on X × X ◊ , is given.
Filomat, 2019
In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, whe... more In this paper, the notion of W-property for subsets of X x X? is introduced and investigated, where X is an Hadamard space and X? is its linear dual space. It is shown that an Hadamard space X is flat if and only if X x X? has W-property. Moreover, the notion of monotone relation from an Hadamard space to its linear dual space is introduced. A characterization result for monotone relations with W-property (and hence in flat Hadamard spaces) is given. Finally, a type of Debrunner-Flor Lemma concerning extension of monotone relations in Hadamard spaces is proved.
This paper is devoted to introduce and investigate the notion of monotone sets in Hadamard spaces... more This paper is devoted to introduce and investigate the notion of monotone sets in Hadamard spaces. First, flat Hadamard spaces are introduced and investigated. It is shown that an Hadamard space $X$ is flat if and only if $X\times X^\medlozenge$ has $\mathcal{F}_l$-property, where $X^\medlozenge$ is the linear dual of $X$. Moreover, monotone and maximal monotone sets are introduced and also monotonicity from polarity point of view is considered. Some characterizations of (maximal) monotone sets, specially based on polarity, is given. Finally, it is proved that any maximal monotone set is sequentially $bw\times${$\|\cdot\|_\loz$}-closed in $X\times X^\medlozenge$.
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Papers by Ali Moslemipour