Porosity and Variational Principles

Marchini, Elsa

Serdica Mathematical Journal (2002)

  • Volume: 28, Issue: 1, page 37-46
  • ISSN: 1310-6600

Abstract

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We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

How to cite

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Marchini, Elsa. "Porosity and Variational Principles." Serdica Mathematical Journal 28.1 (2002): 37-46. <http://eudml.org/doc/11546>.

@article{Marchini2002,
abstract = {We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.},
author = {Marchini, Elsa},
journal = {Serdica Mathematical Journal},
keywords = {Variational Principles; Well-posed Optimization Problems; Porous Sets; Porosity; porosity; variational principles; well-posed optimization problem},
language = {eng},
number = {1},
pages = {37-46},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Porosity and Variational Principles},
url = {http://eudml.org/doc/11546},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Marchini, Elsa
TI - Porosity and Variational Principles
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 1
SP - 37
EP - 46
AB - We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.
LA - eng
KW - Variational Principles; Well-posed Optimization Problems; Porous Sets; Porosity; porosity; variational principles; well-posed optimization problem
UR - http://eudml.org/doc/11546
ER -

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