Characterizations of Nonemptiness and Compactness of the Set of Weakly Efficient Solutions for Convex Vector Optimization and Applications

Huang, Xiaoxu; Yang, Xiaoqi

doi:10.1006/jmaa.2001.7635

Search citation statements

Order By: Relevance

Paper Sections

Select...

By the Hypothesis1

Well-posedness1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2003

2024

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 16 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When (P) is a CVOP, various characterizations of the nonemptiness and compactness can be found in [6]. For generalizations of these characterizations and applications, see [7,11,12].…”

Section: By the Hypothesismentioning

confidence: 99%

See 1 more Smart Citation

Coercivity properties and well-posedness in vector optimization

Deng

2003

RAIRO-Oper. Res.

View full text Add to dashboard Cite

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.

show abstract

“…When (P) is a CVOP, various characterizations of the nonemptiness and compactness can be found in [6]. For generalizations of these characterizations and applications, see [7,11,12].…”

Section: By the Hypothesismentioning

confidence: 99%

“…Since i∈Iλ i f i (x(N )) ≥ p(λ), the inequality (12) implies that p(λ) ≤ p(λ) − /2, which is impossible. This completes the proof.…”

Section: Well-posednessmentioning

confidence: 99%