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Vector variational-like inequalities and vector optimization problems in Asplund spaces

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Abstract

In this paper, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of Mordukhovich limiting subdifferentials are introduced and studied in Asplund spaces. Some relations between the vector variational-like inequalities and vector optimization problems are established by using the properties of Mordukhovich limiting subdifferentials. An existence theorem of solutions for the weak Minty vector variational-like inequality is also given.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China

    Bin Chen & Nan-Jing Huang

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  1. Bin Chen
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  2. Nan-Jing Huang
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Correspondence to Nan-Jing Huang.

Additional information

This work was supported by the Key Program of NSFC (Grant No. 70831005) and the National Natural Science Foundation of China (10671135).

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Chen, B., Huang, NJ. Vector variational-like inequalities and vector optimization problems in Asplund spaces. Optim Lett 6, 1513–1525 (2012). https://doi.org/10.1007/s11590-011-0346-7

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