충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제27권2호
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  • Pages.271-276
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  • 2014
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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A NOTE ON A REGULARIZED GAP FUNCTION OF QVI IN BANACH SPACES

  • Kum, Sangho (Department of Mathematics Education Chungbuk National University)
  • 투고 : 2014.02.14
  • 심사 : 2014.04.16
  • 발행 : 2014.05.15
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초록

Recently, Taji [7] and Harms et al. [4] studied the regularized gap function of QVI analogous to that of VI by Fukushima [2]. Discussions are made in a finite dimensional Euclidean space. In this note, an infinite dimensional generalization is considered in the framework of a reflexive Banach space. To do so, we introduce an extended quasi-variational inequality problem (in short, EQVI) and a generalized regularized gap function of EQVI. Then we investigate some basic properties of it. Our results may be regarded as an infinite dimensional extension of corresponding results due to Taji [7].

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참고문헌

  1. G. Y. Chen, C. J. Goh, and X. Q. Yang, On gap functions and duality of variational inequality problems, J. Math. Anal. Appl. 214 (1997), 658-673. https://doi.org/10.1006/jmaa.1997.5608
  2. M. Fukushima, Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems, Math. Programming 53 (1992), 99-110. https://doi.org/10.1007/BF01585696
  3. F. Giannessi, Separation of sets and gap functions for quasi-variational inequalities, in F. Giannessi and A. Maugeri (eds.): Variational Inequality and Network Equilibrium Problems, Plenum Press, New York, 1995, 101-121.
  4. N. Harms, C. Kanzow, and O. Stein, Smoothness properties of a regularized gap function for quasi-variational inequalities, to appear in Optim. Meth. Software.
  5. W. W. Hogan, Point-to-set maps in mathematical programming, SIAM Rev. 15 (1973), 591-603. https://doi.org/10.1137/1015073
  6. S. H. Kum and G. M. Lee, On gap functions of variational inequalty in a Banach space, J. Korean Math. Soc. 38 (2001), 683-695.
  7. K. Taji, On gap functions for quasi-variational inequalities, Abstr. Appl. Anal. (2008), Article ID 531361.

피인용 문헌

  1. A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI vol.28, pp.1, 2015, https://doi.org/10.14403/jcms.2015.28.1.145