TY - JOUR
T1 - On Variational Principles, Level Sets, Well-Posedness, and ε-Solutions in Vector Optimization
AU - Dentcheva, D.
AU - Helbig, S.
PY - 1996/5
Y1 - 1996/5
N2 - Using the concept for ε-efficient solutions introduced in Refs. 1 and 2, we extend the Ekeland variational principle and another variational principle given in Ref. 3 to vector-valued objective functions. This enables us to establish a kind of well-posedness for the resulting perturbed vector optimization problems. Based on this definition of ε-efficiency, we also formulate a concept for level sets and prove some results about the Kuratowski limits of level sets.
AB - Using the concept for ε-efficient solutions introduced in Refs. 1 and 2, we extend the Ekeland variational principle and another variational principle given in Ref. 3 to vector-valued objective functions. This enables us to establish a kind of well-posedness for the resulting perturbed vector optimization problems. Based on this definition of ε-efficiency, we also formulate a concept for level sets and prove some results about the Kuratowski limits of level sets.
KW - Nonlinear vector optimization
KW - Variational principles
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=0347141428&partnerID=8YFLogxK
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U2 - 10.1007/BF02192533
DO - 10.1007/BF02192533
M3 - Article
AN - SCOPUS:0347141428
SN - 0022-3239
VL - 89
SP - 325
EP - 349
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 2
ER -