# Coercivity properties and well-posedness in vector optimization

RAIRO - Operations Research - Recherche Opérationnelle (2003)

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

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topDeng, 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 -

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