SCALARIZATION METHODS FOR MINTY-TYPE VECTOR VARIATIONAL INEQUALITIES
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초록
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 set-valued 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].
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 set-valued 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].
참고문헌 (11)
- G. Y. Chen, "Vector optimization: Set-valued Variational Analysis" (2005), Springer-Verlag
- F. Giannessi, "Vector Variational Inequalities and Vector Theory Variational Equilib-rium" (2000), Kluwer Academic Publishers
- F. Giannessi, "On the theory of vector optimization and variational inequalities. Image space analysis and separation. in: Vector variational Inequalities and Vector Equilibria", pp.153~215 (2000), Kluwer Academic Publishers
- S.-M. Guu, "Scalarization approaches for set-valued vector opti-mization problems and vector variational inequalities", J. Math. Anal. Appl., 356, pp.564~576 (2009)
- N. Hadjesavvas, "Quasimonotonicity and pseudomonotonicity in vari- ational inequalities and equilibrium problem: In Generalized Convexity Generalized Monotonicity", pp.257~275 (1998), Academic Publishers
- B. Jimenez, "Scalarization and optimality conditions for strict minimizers in multiobjective optimization via contingent epiderivatives", J. Math. Anal. Appl., 352, pp.788~798 (2009)
- H. Kneser, "Sur un theoreme fundamental dela theorie des Jeux", C. R. Acad. Sci. Paris, 234, pp.2418~2420 (1952)
- I. V. Konnov, "A scalarization approach for variational inequalities with applications", J. Global Optim., 32, pp.517~527 (2005)
- B.-S. Lee, "Scalarization methods for vector variational inequalities", ~
- Z. B. Liu, "Scalarization approaches for generalized vector variational inequalities", Nonlinear Anal. Forum, 12(1), pp.119~124 (2007)
- Z. D. Slavov, "Scalarization techniques or relationship between a social welfare function and a Pareto optimality concept", Appl. Math. & Comp., 172, pp.464~471 (2006)