On the Equivalence of Weak- and Cyclic-Monotonicity

On the Subdifferentials of Quasiconvex and Pseudoconvex Functions and Cyclic Monotonicity

Journal of Mathematical Analysis and Applications ◽

10.1006/jmaa.1999.6437 ◽

1999 ◽

Vol 237 (1) ◽

pp. 30-42 ◽

Cited By ~ 34

Author(s):

Aris Daniilidis ◽

Nicolas Hadjisavvas

Keyword(s):

Cyclic Monotonicity ◽

Pseudoconvex Functions

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Equivalence betweenp-cyclic quasimonotonicity andp-cyclic monotonicity of affine maps

Optimization ◽

10.1080/02331934.2014.891031 ◽

2014 ◽

Vol 64 (7) ◽

pp. 1487-1497

Author(s):

Eladio Ocaña ◽

John Cotrina ◽

Orestes Bueno

Keyword(s):

Affine Maps ◽

Cyclic Monotonicity

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Maximal monotonicity and cyclic monotonicity arising in nonsmooth Lur'e dynamical systems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2016.11.025 ◽

2017 ◽

Vol 448 (1) ◽

pp. 691-706 ◽

Cited By ~ 4

Author(s):

Samir Adly ◽

Abderrahim Hantoute ◽

Ba Khiet Le

Keyword(s):

Dynamical Systems ◽

Maximal Monotonicity ◽

Cyclic Monotonicity

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Fitzpatrick functions, cyclic monotonicity and Rockafellar’s antiderivative

Nonlinear Analysis ◽

10.1016/j.na.2006.01.013 ◽

2007 ◽

Vol 66 (5) ◽

pp. 1198-1223 ◽

Cited By ~ 40

Author(s):

Sedi Bartz ◽

Heinz H. Bauschke ◽

Jonathan M. Borwein ◽

Simeon Reich ◽

Xianfu Wang

Keyword(s):

Cyclic Monotonicity ◽

Fitzpatrick Functions

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Subdifferentials of convex functions and sigma-cyclic monotonicity

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700022279 ◽

2000 ◽

Vol 61 (2) ◽

pp. 269-276 ◽

Cited By ~ 1

Author(s):

Aris Daniilidis

Keyword(s):

Hilbert Space ◽

Monotone Operator ◽

Convex Functions ◽

Monotone Operators ◽

Cyclic Monotonicity ◽

Densely Defined

The property of σcyclic monotonicity is proposed here to describe subdifferentials of lsc convex functions that are continuous in their domains. It is shown that all monotone operators in R and all densely defined cyclically monotome operators in Rn share this property. Examples of a densely defined maximal cyclically monotone operator in a Hilbert space and of a subdifferential of a convex lsc function in R2 which are not σ-cyclically monotone operators are given.

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