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Relationships between interval-valued vector optimization problems and vector variational inequalities

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Abstract

In this paper, we study some relationships between interval-valued vector optimization problems and vector variational inequalities under the assumptions of LU-convex smooth and non-smooth objective functions. We identify the weakly efficient points of the interval-valued vector optimization problems and the solutions of the weak vector variational inequalities under smooth and non-smooth LU-convexity assumptions.

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Acknowledgments

The authors would like to thank the referees for careful reading and valuable suggestions that has improved the paper in its present form. This work was partially supported by Natural Science Basic Research Plan in Shaanxi Province of China (Program Nos. 2013JQ1020, 2013KJXX-29, 2014 JM8307), National Natural Science Foundation of China (Program Nos. 11301415, 61100166, 61303 092, 11401469, 11426176, 11401357), Special funds for the construction of key disciplines funded projects in Shaanxi Province, Project funded by China Postdoctoral Science Foundation (No.2014M552453), Hanzhong administration of science and technology under Grant No. 2013hzzx-39, National Key Technologies R&D Program of China under Grant No. 2012BAH16F02, Foundation from Xi’an University of Posts & Telecommunications for Young Teachers: ZL2014-34, and the Science Plan Foundations of the Education Bureau of Shaanxi Province (Nos.11JK1051, 2013JK1098, 2013JK1130, 2013JK1182, 14JK1661).

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Authors and Affiliations

  1. Department of Computers, Xi’an Jiaotong University, Xi’an, China

    Jianke Zhang & Qinghua Zheng

  2. Department of Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, China

    Jianke Zhang, Xiaojue Ma & Lifeng Li

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  1. Jianke Zhang
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  2. Qinghua Zheng
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  3. Xiaojue Ma
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  4. Lifeng Li
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Correspondence to Jianke Zhang.

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Zhang, J., Zheng, Q., Ma, X. et al. Relationships between interval-valued vector optimization problems and vector variational inequalities. Fuzzy Optim Decis Making 15, 33–55 (2016). https://doi.org/10.1007/s10700-015-9212-x

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  • DOI: https://doi.org/10.1007/s10700-015-9212-x

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