Invited Session Fri.3.H 2051

Friday, 15:15 - 16:45 h, Room: H 2051

Cluster 24: Variational analysis [...]

Monotone operators


Chair: Radu Ioan Bot



Friday, 15:15 - 15:40 h, Room: H 2051, Talk 1

Radu Ioan Bot
Approaching the maximal monotonicity of bifunctions via representative functions

Coauthor: Sorin-Mihai Grad


In this talk we provide an approach to maximal monotone bifunctions by means of the theory of representative functions. Thus we extend to nonreflexive Banach spaces recent results due to A.,N. Iusem (Journal of Convex Analysis, 2011) and, respectively, N. Hadjisavvas and H. Khatibzadeh (Optimization, 2010), where sufficient conditions guaranteeing the maximal monotonicity of bifunctions were introduced.



Friday, 15:45 - 16:10 h, Room: H 2051, Talk 2

Marco Rocco
On a surjectivity-type property of maximal monotone operators

Coauthor: Juan Enrique Martínez-Legaz


In this paper we carry on the inquiry into surjectivity and related properties of maximal monotone operators initiated in Martínez-Legaz, Some generalizations of Rockafellar’s surjectivity theorem (Pac. J. Optim., 2008) and Rocco and Martínez-Legaz, On surjectivity results for maximal monotone operators of type (D) (J. Convex Anal., 2011). Providing a correction to a previous result, we obtain a new generalization of the surjectivity theorem for maximal monotone operators.



Friday, 16:15 - 16:40 h, Room: H 2051, Talk 3

Szilárd László
Regularity conditions for the maximal monotonicity of the generalized parallel sum


We give several regularity conditions, both closedness and interior point type, that ensure the maximal monotonicity of the generalized parallel sum of two strongly representable maximal monotone operators, and we extend some recent results concerning on the same problem.
Our results are based on the concepts of representative function and Fenchel conjugate, while the technique used to establish closedness type, respectively interior-point type regularity conditions, that ensure the maximal monotonicity of this generalized parallel sum, is stable strong duality.
We give an useful application of the stable strong duality for the problem involving the function fº A+g, where
f and g are proper, convex and lower semicontinuous functions, and A is a linear and continuous operator. We
also introduce some new generalized infimal convolution formulas, and establish some results concerning on their
Fenchel conjugate.


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