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

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Abstract

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.

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Acknowledgements

The authors would like to thank anonymous referees for their valuable remarks and suggestions which have helped us improve the paper. This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2020.11.

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Authors and Affiliations

  1. Department of Mathematics, Teacher College, Cantho University, Cantho, Vietnam

    Lam Quoc Anh

  2. University of Science, Ho Chi Minh City, Vietnam

    Pham Thanh Duoc

  3. Vietnam National University, Ho Chi Minh City, Vietnam

    Pham Thanh Duoc

  4. Department of Mathematics, Vo Truong Toan University, Haugiang, Vietnam

    Pham Thanh Duoc

  5. Department of Mathematics, Cantho University, Cantho, Vietnam

    Tran Thi Thuy Duong

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  1. Lam Quoc Anh
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  2. Pham Thanh Duoc
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  3. Tran Thi Thuy Duong
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Correspondence to Pham Thanh Duoc.

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Anh, L.Q., Duoc, P.T. & Duong, T.T.T. Connectedness properties of the efficient sets and the nondominated sets to vector optimization problems. Optim Lett 16, 2457–2468 (2022). https://doi.org/10.1007/s11590-021-01841-x

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