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A new class of generalized convex programming

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Abstract

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is η-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

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References

  1. M. A. Hanson,On sufficiency of the Kuhn-Tucker condition, J.Math. Anal. Appl.80 (1981), 545–550.

    Article  MATH  MathSciNet  Google Scholar 

  2. C. R. Bector,B-vex functions, J. Math. Anal. Appl.71 (1991), 237–253.

    MATH  MathSciNet  Google Scholar 

  3. C. R. Bector,Generalization of Preinvex and B-vex functions, JOTA,76 (1993), 577–587.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. P. Vial,Strong convexity of sets and functions, J. Math. Econon.9 (1982), 187–205.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. P. Vial,Strong and weak convexity of sets and functions, Math. Oper. Pes.8 (1983), 231–259.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. A. Hanson and B. Mond,Further generalizations of convexity in mathematical programming, J. Inform, Optim. sei3 (1982), 22–35.

    MathSciNet  Google Scholar 

  7. Vasile Preda,On efficiency and duality for multiobjective programs, JOMAA166 (1992), 365–377.

    MATH  MathSciNet  Google Scholar 

  8. N. G. Rueda and M. A. Hanson,Optimality criteria in mathematical programming involving generalized invexity, JOMAA130 (1988), 375–385.

    MATH  MathSciNet  Google Scholar 

  9. M. A. Hanson and B. Mond,Necessary and sufficient conditions in constrained optimization, 1984.

  10. D. H. Martin,The essence of invexity, JOTA47 (1985), 65–76.

    Article  MATH  Google Scholar 

  11. M. S. Bazaraa and C. M. Shetty,Nonlinear programming theory and algorithm, John Wiley and Sons, Inc, New York, 1979.

    Google Scholar 

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Authors and Affiliations

  1. School of Science, Jinan University, 250022, Jinan, P. R. China

    Zhaoxiang Yan

  2. Department of Mathematics, Shandong Normal University, 250014, Jinan, P. R. China

    Shizheng Li

Authors
  1. Zhaoxiang Yan
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  2. Shizheng Li
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Additional information

Zhaoxiang Yan received his B. A. D. and M. A. D. from Shandong Normal University respectively in 1996 and 1999. He majored in the theory of graph and programming. Since 1999 he has worked in Jinan University and became a lecturer. Now he is a doctoral candidate and the changed the research direction to cryptography.

Shizheng Li is a professor and a master tutor of Shandong Normal University. He is famous in Chinese academic circles. He has ever been engagaed in the National Natural Science Fund project.

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Yan, Z., Li, S. A new class of generalized convex programming. JAMC 17, 351–360 (2005). https://doi.org/10.1007/BF02936061

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  • DOI: https://doi.org/10.1007/BF02936061

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