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Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints

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  • San-hua Wang
  • Nan-jing Huang
  • Donal O’Regan

Abstract

In this paper, well-posedness of generalized quasi-variational inclusion problems and of optimization problems with generalized quasi-variational inclusion problems as constraints is introduced and studied. Some metric characterizations of well-posedness for generalized quasi-variational inclusion problems and for optimization problems with generalized quasi-variational inclusion problems as constraints are given. The equivalence between the well-posedness of generalized quasi-variational inclusion problems and the existence of solutions of generalized quasi-variational inclusion problems is given under suitable conditions. Copyright Springer Science+Business Media, LLC. 2013

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  • San-hua Wang & Nan-jing Huang & Donal O’Regan, 2013. "Well-posedness for generalized quasi-variational inclusion problems and for optimization problems with constraints," Journal of Global Optimization, Springer, vol. 55(1), pages 189-208, January.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:1:p:189-208
    DOI: 10.1007/s10898-012-9980-6
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    1. Fang, Ya-Ping & Huang, Nan-Jing & Yao, Jen-Chih, 2010. "Well-posedness by perturbations of mixed variational inequalities in Banach spaces," European Journal of Operational Research, Elsevier, vol. 201(3), pages 682-692, March.
    2. G. P. Crespi & A. Guerraggio & M. Rocca, 2007. "Well Posedness in Vector Optimization Problems and Vector Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 213-226, January.
    3. M. Durea, 2007. "Scalarization for pointwise well-posed vectorial problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 409-418, December.
    4. M. B. Lignola, 2006. "Well-Posedness and L-Well-Posedness for Quasivariational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 119-138, January.
    5. Gábor Kassay, 2010. "On Equilibrium Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 55-83, Springer.
    6. B. Lemaire & C. Ould Ahmed Salem & J. P. Revalski, 2002. "Well-Posedness by Perturbations of Variational Problems," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 345-368, November.
    7. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    8. M. Margiocco & F. Patrone & L. Pusillo, 2002. "On the Tikhonov Well-Posedness of Concave Games and Cournot Oligopoly Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 361-379, February.
    9. M. Bianchi & G. Kassay & R. Pini, 2009. "Well-posedness for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 171-182, August.
    10. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
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    Cited by:

    1. M. Darabi & J. Zafarani, 2015. "Tykhonov Well-Posedness for Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 458-479, May.
    2. J. W. Chen & Y. J. Cho & S. A. Khan & Z. Wan & C. F. Wen, 2015. "The Levitin-Polyak well-posedness by perturbations for systems of general variational inclusion and disclusion problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(6), pages 901-920, December.

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