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On general vector quasi-optimization problems

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  • Angelo Guerraggio
  • Nguyen Xuan Tan

Abstract

Vector general quasi-optimization problems are formulated and some sufficient conditions on the existence of solutions for these problems are shown. These concern the existence of solutions, the stability and the structure of solution set of general vector problems. As special case, we obtain results on the existence of solutions of vector quasi-optimization problem. Some relationships between these problems and others, as vector quasi-equilibrium problems, quasi-variational inequalities, complementarity problems,..., are shown. From these we extend some well-known results obtained by Blum and Oettli [4], Park [21], Chan and Pang [6], Parida and Sen [20], Browder and Minty [18], Fan [8], etc. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • Angelo Guerraggio & Nguyen Xuan Tan, 2002. "On general vector quasi-optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(3), pages 347-358, June.
    • Handle: RePEc:spr:mathme:v:55:y:2002:i:3:p:347-358
    DOI: 10.1007/s001860200212
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    Citations

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    Cited by:

    1. N. X. Hai & P. Q. Khanh, 2007. "Systems of Set-Valued Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 55-67, October.
    2. N. X. Hai & P. Q. Khanh, 2007. "Existence of Solutions to General Quasiequilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 317-327, June.
    3. N. Minh & N. Tan, 2006. "On the Existence of Solutions of Quasi-equilibrium Problems with Constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(1), pages 17-31, August.
    4. D. T. Luc, 2008. "An Abstract Problem in Variational Analysis," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 65-76, July.
    5. H. Mohebi & M. Vatandoost, 2011. "Counterexamples on some articles on quasi-variational inclusion problems," Journal of Global Optimization, Springer, vol. 49(4), pages 707-712, April.
    6. N. X. Tan, 2004. "On the Existence of Solutions of Quasivariational Inclusion Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 619-638, December.

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