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Solvability and boundedness for general variational inequality problems

Gui-Mei Luo
대한수학회 (The Korean Mathematical Society)|2013.03|대한수학회보 (Bulletin of the KMS)|제50권 제2호|pp. 589-599

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키워드

existenceboundednessgeneral variational inequality problemgeneral complementarity problemstrict feasibilityquasi-g-PM * function
주제분류수학

초록

In this paper, we propose a sufficient condition for the exis- tence of solutions to general variational inequality problems (GV I(K, F, g)). The condition is also necessary when F is a g-PM * function. We also investigate the boundedness of the solution set of (GV I(K, F, g)). Furthermore, we show that when F is norm-coercive, the general com- plementarity problems (GCP(K, F, g)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, g)).

Abstract

In this paper, we propose a sufficient condition for the exis- tence of solutions to general variational inequality problems (GV I(K, F, g)). The condition is also necessary when F is a g-PM * function. We also investigate the boundedness of the solution set of (GV I(K, F, g)). Furthermore, we show that when F is norm-coercive, the general com- plementarity problems (GCP(K, F, g)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, g)).

참고문헌 (26)

  1. G. Y. Chen, "On gap functions and duality of variational inequality problems", J. Math. Anal. Appl, 214(2), pp.658~673 (1997)
  2. F. Facchinei, "On generalized Nash games and variational inequalities", Oper. Res. Lett, 35(2), pp.159~164 (2007)
  3. F. Facchinei, "Finite-Dimensional Variational Inequalities and Comple- mentarity Problems, Vol. I and II" (2003), Springer-Verlag
  4. M. Fakhar, "On generalized variational inequalities", J. Global Optim, 43(4), pp.503~511 (2009)
  5. J. Han, "Solvability of variational inequality problems", J. Optim. Theory Appl, 122(3), pp.501~520 (2004)
  6. P. T. Harker, "Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications", Math. Programming, 48(2), pp.161~220 (1990)
  7. B. S. He, "A class of projection and contraction methods for monotone variational in- equalities", Appl. Math. Optim, 35(1), pp.69~76 (1997)
  8. B. S. He, "Improvement of some projection methods for monotone non- linear variational inequalities", J. Optim. Theory Appl, 112(1), pp.111~128 (2002)
  9. Z. H. Huang, "Sufficient conditions on nonemptiness and boundedness of the solution set of the P0 function nonlinear complementarity problem", Oper. Res. Lett, 30(3), pp.202~210 (2002)
  10. Z. H. Huang, "Generalization of an existence theorem for variational inequalities", J. Optim. Theory Appl, 118(3), pp.567~585 (2003)
  11. Z. Liu, "Exceptional family of elements for generalized variational inequalities", J. Global Optim, 48(3), pp.465~471 (2010)
  12. D. T. Luc, "The Frechet approximate Jacobian and local uniqueness in variational in- equalities", J. Math. Anal. Appl, 268(2), pp.629~646 (2002)
  13. D. T. Luc, "Local uniqueness of solutions of general variational inequalities", J. Optim. Theory Appl, 117(1), pp.103~119 (2003)
  14. M. A. Noor, "General variational inequalities", Appl. Math. Lett, 1(2), pp.119~122 (1988)
  15. M. A. Noor, "Wiener-Hopf equations and variational inequalities", J. Optim. Theory Appl, 79(1), pp.197~206 (1993)
  16. M. A. Noor, "Some developments in general variational inequalities", Appl. Math. Comput, 152(1), pp.199~277 (2004)
  17. M. A. Noor, "Extended general variational inequalities", Appl. Math. Lett, 22(2), pp.182~186 (2009)
  18. M. A. Noor, "Some aspects of extended general variational inequalities", Abstract and Applied Analysis, pp.303569~ (2012)
  19. J. S. Pang, "Quasi-variational inequalities, generalized Nash equilibria, and multileader-follower games", Comput. Manag. Sci, 2(1), pp.21~56 (2005)
  20. J. S. Pang, "On a generalization of a normal map and equation", SIAM J. Control Optim, 33(1), pp.168~184 (1995)
  21. N. H. Xiu, "Tangent projection equations and general variational inequalities", J. Math. Anal. Appl, 258(2), pp.755~762 (2001)
  22. J. C. Yao, "A basic theorem of complementarity for the generalized variational-like in- equality problem", J. Math. Anal. Appl, 158(1), pp.124~138 (1991)
  23. J. C. Yao, "On the general variational inequality", J. Math. Anal. Appl, 174(2), pp.550~555 (1993)
  24. L. Yu, "Convergence theorems of solutions of a generalized variational inequality", Fixed Point Theory Appl, 2011(19), pp.10~ (2011)
  25. Y. B. Zhao, "Exceptional family of elements for a variational inequality problem and its applications", J. Global Optim, 14(3), pp.313~330 (1999)
  26. Y. B. Zhao, "An alternative theorem for generalized variational inequal- ities and solvability of nonlinear quasi-PM * complementarity problems", Appl. Math. Comput, 109(2), pp.167~182 (2000)

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