DOI QR코드

DOI QR Code

A REMARK ON THE REGULARIZED GAP FUNCTION FOR IQVI

  • Kum, Sangho (Department of Mathematics Education Chungbuk National University)
  • Received : 2015.01.09
  • Accepted : 2015.01.26
  • Published : 2015.02.15

Abstract

Aussel et al. [1] introduced the notion of inverse quasi-variational inequalities (IQVI) by combining quasi-variational inequalities and inverse variational inequalities. Discussions are made in a finite dimensional Euclidean space. In this note, we develop an infinite dimensional version of IQVI by investigating some basic properties of the regularized gap function of IQVI in a Banach space.

Keywords

References

  1. D. Aussel, R. Gupta, and A. Mehra Gap functions and error bounds for inverse quasi-variational inequality problems, J. Math. Anal. Appl. 407 (2013), 270-280. https://doi.org/10.1016/j.jmaa.2013.03.049
  2. C. Berge, Topological spaces, Oliver and Boyd Ltd, London, 1963.
  3. 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
  4. 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.
  5. N. Harms, C. Kanzow, and O. Stein, Smoothness properties of a regularized gap function for quasi-variational inequalities, Optim. Meth. Software. 29 (2014), 720-750. https://doi.org/10.1080/10556788.2013.841694
  6. Q. Han and B. S. He, A predict-correct projection method for monotone variant variational inequalities, Chin. Sci. Bull. 43 (1998), 1264-1267. https://doi.org/10.1007/BF02884138
  7. X. He and H. X. Liu, Inverse variational inequalities with projection-based solution methods, Eur. J. Oper. Res. 208 (2011), 12-18. https://doi.org/10.1016/j.ejor.2010.08.022
  8. S. H. Kum, A note on a regularized gap function of QVI in Banach spaces, J. Chungcheong Math. Soc. 27 (2014), 271-276. https://doi.org/10.14403/jcms.2014.27.2.271
  9. R. R. Phelps, Convex Functions, Monotone Operators and Differentiability, 2nd ed., Lecture Notes in Mathematics, Vol. 1364 Springer-Verlag, Berlin/New York, 1993.