Connectedness properties of the efficient sets and the nondominated sets to vector optimization problems

In this paper we consider vector optimization problems in normed spaces. First, we propose three generalized concepts related to convexity conditions and discuss their relationships with classical ones. Next, based on Hiriart-Urruty oriented distance function, we introduce a new nonlinear scalarizat...

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Bibliographic Details
Published in:Optimization letters 2022-11, Vol.16 (8), p.2457-2468
Main Authors: Anh, Lam Quoc, Duoc, Pham Thanh, Duong, Tran Thi Thuy
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
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Summary:In this paper we consider vector optimization problems in normed spaces. First, we propose three generalized concepts related to convexity conditions and discuss their relationships with classical ones. Next, based on Hiriart-Urruty oriented distance function, we introduce a new nonlinear scalarization function for the reference problems and study its properties. Finally, employing this function and the proposed concepts, we address connectedness conditions for efficient and nondominated sets to vector optimization problems.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-021-01841-x