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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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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DOI: https://doi.org/10.1007/s11590-011-0346-7