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http://dx.doi.org/10.7858/eamj.2010.26.3.415

SCALARIZATION METHODS FOR MINTY-TYPE VECTOR VARIATIONAL INEQUALITIES  

Lee, Byung-Soo (DEPARTMENT OF MATHEMATICS KYUNGSUNG UNIVERSITY)
Publication Information
East Asian mathematical journal / v.26, no.3, 2010 , pp. 415-421 More about this Journal
Abstract
Many kinds of Minty's lemmas show that Minty-type variational inequality problems are very closely related to Stampacchia-type variational inequality problems. Particularly, Minty-type vector variational inequality problems are deeply connected with vector optimization problems. Liu et al. [10] considered vector variational inequalities for setvalued mappings by using scalarization approaches considered by Konnov [8]. Lee et al. [9] considered two kinds of Stampacchia-type vector variational inequalities by using four kinds of Stampacchia-type scalar variational inequalities and obtain the relations of the solution sets between the six variational inequalities, which are more generalized results than those considered in [10]. In this paper, the author considers the Minty-type case corresponding to the Stampacchia-type case considered in [9].
Keywords
Minty-type scalar variational inequalities; Minty-type vector variational inequalities; scalarization approach; Kneser Minimax Theorem;
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