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A sufficient condition that has no exceptional family of elements for SDCP

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Abstract

In this paper, we introduce a novel sufficient existence condition that has no exceptional family of elements for semidefinite complementarity problem. In addition, we give a particular example to show that the new condition is not stronger than Isac–Carbone’s condition.

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References

  1. Isac, G., Bulavaski, V., Kalashnikov, V.V.: Exceptional families, topological degree and complementarity problems. J. Glob. Optim. 10, 207–225 (1997)

    Article  MATH  Google Scholar 

  2. Kalashnikov, V.V.: Complementarity problem and the generalized oligopoly model. Habilitation Thesis, CEMI, Moscow (1995) (in Russian)

  3. Isac, G., Carbone, A.: Exceptional families of elements for continuous functions: some applications to complementarity theory. J. Glob. Optim. 15, 181–196 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  4. Zhang, L.: Solvability of semidefinite complementarity problems. Appl. Math. Comput. 196, 86–93 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hua, Q., Ouyang, Z., Wang, Z.: Exceptional family and solvability of copositive complementarity problems. J. Math. Anal. Appl. 388, 519–524 (2012)

    Article  MathSciNet  Google Scholar 

  6. Smith, T.E.: A solution condition for complementarity problems, with an application to spatial price equilibrium. Appl. Math. Comput. 15, 61–69 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  7. Isac, G., Obuchowska, W.T.: Functions without exceptional family of elements and complementarity problems. J. Optim. Theory Appl. 99, 147–163 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Isac, G., Bulavski, V., Kalashnikov, V.: Exceptional families, topological degree and complementarity problems. J. Glob. Optim. 10, 207–225 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tseng, P.: Merit functions for semidefinite complementarity problems. Math. Program. 83, 159–185 (1998)

    MATH  Google Scholar 

  10. Bulavaski, V., Isac, G., Kalashnikov, V.: Application of topological degree theory to semidefinite complementarity problem. Optimization 49, 405–423 (2001)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

The project supported by National Natural Science Foundation of China (Grant No. 11071041) and Fujian Natural Science Foundation (Grant No. 2009J01002).

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    Na Huang & Changfeng Ma

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  1. Na Huang
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  2. Changfeng Ma
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Correspondence to Changfeng Ma.

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Huang, N., Ma, C. A sufficient condition that has no exceptional family of elements for SDCP. Optim Lett 8, 259–265 (2014). https://doi.org/10.1007/s11590-012-0569-2

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  • DOI: https://doi.org/10.1007/s11590-012-0569-2

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