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.
@article{RO_2003__37_3_195_0,
author = {Deng, Sien},
title = {Coercivity properties and well-posedness in vector optimization},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {195--208},
year = {2003},
publisher = {EDP Sciences},
volume = {37},
number = {3},
doi = {10.1051/ro:2003021},
mrnumber = {2034539},
zbl = {1070.90095},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro:2003021/}
}
TY - JOUR AU - Deng, Sien TI - Coercivity properties and well-posedness in vector optimization JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2003 SP - 195 EP - 208 VL - 37 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro:2003021/ DO - 10.1051/ro:2003021 LA - en ID - RO_2003__37_3_195_0 ER -
%0 Journal Article %A Deng, Sien %T Coercivity properties and well-posedness in vector optimization %J RAIRO - Operations Research - Recherche Opérationnelle %D 2003 %P 195-208 %V 37 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro:2003021/ %R 10.1051/ro:2003021 %G en %F RO_2003__37_3_195_0
Deng, Sien. Coercivity properties and well-posedness in vector optimization. RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 3, pp. 195-208. doi: 10.1051/ro:2003021
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