Coercivity properties and well-posedness in vector optimization

Sien Deng

RAIRO - Operations Research - Recherche Opérationnelle (2003)

  • Volume: 37, Issue: 3, page 195-208
  • ISSN: 0399-0559

Abstract

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This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems. In particular we show that a well-known relative interiority condition can be used as a sufficient condition for well-posedness in convex vector optimization.

How to cite

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Deng, Sien. "Coercivity properties and well-posedness in vector optimization." RAIRO - Operations Research - Recherche Opérationnelle 37.3 (2003): 195-208. <http://eudml.org/doc/244920>.

@article{Deng2003,
abstract = {This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems. In particular we show that a well-known relative interiority condition can be used as a sufficient condition for well-posedness in convex vector optimization.},
author = {Deng, Sien},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {vector optimization; weakly efficient solution; well posedness; level-coercivity; error bounds; relative interior; well-posedness},
language = {eng},
number = {3},
pages = {195-208},
publisher = {EDP-Sciences},
title = {Coercivity properties and well-posedness in vector optimization},
url = {http://eudml.org/doc/244920},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Deng, Sien
TI - Coercivity properties and well-posedness in vector optimization
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 3
SP - 195
EP - 208
AB - This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems. In particular we show that a well-known relative interiority condition can be used as a sufficient condition for well-posedness in convex vector optimization.
LA - eng
KW - vector optimization; weakly efficient solution; well posedness; level-coercivity; error bounds; relative interior; well-posedness
UR - http://eudml.org/doc/244920
ER -

References

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