Abstract
The aim of this paper is to study a link between the optimal points of vector optimization problems governed by set-valued maps and the solutions of some related generalized variational inequalities. The main results of the paper describe necessary existence conditions for the variational inequalities under study in terms of generalized differentiation objects, in the case of standard fixed order structure, as well as in the case of variable order structure. For the fulfillment of all necessary steps in our investigation, we present a new approach based on meaningful results concerning the openness for finite families of set-valued mappings and the penalization of constrained vector optimization problems.
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The authors thank the anonymous referees for their constructive remarks.
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Dedicated to Professor Michel Théra in honor of his 70th birthday.
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Durea, M., Florea, EA. A Study of Generalized Vector Variational Inequalities via Vector Optimization Problems. Vietnam J. Math. 46, 33–52 (2018). https://doi.org/10.1007/s10013-017-0257-8
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DOI: https://doi.org/10.1007/s10013-017-0257-8
Keywords
- Vector variational inequalities
- Vector optimization
- Penalization
- Fixed and variable ordering structures
- Necessary existence conditions