Invited Session Thu.3.H 2051

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

Cluster 24: Variational analysis [...]

Semi-continuous programming

 

Chair: Wilfredo Sosa

 

 

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

Ademir Alves Ribeiro
Fenchel-Moreau conjugation for lower semi-continuous functions

Coauthors: John Cotrina, Elizabeth Wegner Karas, Wilfredo Sosa, Yuan Jin Yun

 

Abstract:
We introduce a modification of Fenchel's conjugation which is a
particular case of Moreau's conjugation. We obtain nice properties
as convexity of the conjugate function even though the function is
not convex. We also introduce the concept of conjugate dual space
as a class of continuous operators, while in the Fenchel's
conjugation, the conjugate dual space is the classical topological
dual space. Finally we present some examples for illustrating the
difference between the Fenchel-Moreau's conjugation and our
modification.

 

 

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

Fernanda M. P. Raupp
A duality scheme for semi-continuous programming

Coauthors: John Cotrina, Wilfredo Sosa

 

Abstract:
We introduce a duality scheme for the class of mathematical programming problems called Semi-Continuous Programming (SCP), which contains constrained minimization problems with lower semi-continuous objective functions. We study some solution existence conditions for SCP based on asymptotic techniques. Then, we devise the duality scheme for the SCP problem through the construction of an auxiliary function and the application of a modification of the Fenchel-Moreau conjugation. We show that the dual problem associated to the SCP problem is convex and, particularly, we devise a dual problem for the minimization of any quadratic function constrained to a polyhedral set.

 

 

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

Wilfredo Sosa
Separation theorems for closed sets

 

Abstract:
In this paper we introduce some separation theorems for disjoint
closed nonempty sets. The proposed theoretical results differ from
the ones in the literature, in particular from Urisohn's and Michael's
results, mainly by making use of special continuous functions (in fact,
this class of special continuous functions is a dense subspace of the
continuous functions space with the domain being a Hilbert space and
real values) instead of considering just the space of all these continuous
functions. As an application we reconstruct the conjugation for lower
semi-continuous functions.

 

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