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Another approach to multiobjective programming problems withF-convex functions

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Abstract

In this paper, optimality conditions for multiobjective programming problems havingF-convex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function. Furthermore, anF—Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of a saddle point are given.

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References

  1. S. Brumelle,Duality for multiple objective convex programs, Mathematics of Operations Research6 (1981), 159–172.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. N. Das and S. Nanda,Proper efficiency conditions and duality for multiobjective programming problems involving semilocally invex functions, Optimization34 (1985), 43–51.

    Article  MathSciNet  Google Scholar 

  3. M. A. Geoffrion,Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications22 (1968), 613–630.

    Article  MathSciNet  Google Scholar 

  4. E. H. Ivanov and R. Nehse,Some results on dual vector optimization problems, Optimization4 (1985), 505–517.

    Article  MathSciNet  Google Scholar 

  5. P. Kanniappan,Necessary conditions for optimality of nondifferentiable convex multiobjective programming, Journal of Optimization Theory and Applications40 (1983), 167–174.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. Ruiz-Canales and A. Rufián-Lizana,A characterization of weakly efficient points, Mathematical Programming68 (1995), 205–212.

    MathSciNet  Google Scholar 

  7. T. Weir, B. Mond and B. D. Craven,On duality for weakly minimized vector valued optimization problems, Optimization17 (1986), 711–721.

    Article  MATH  MathSciNet  Google Scholar 

  8. T. Weir and B. Mond,Generalized convexity and duality in multiple objective programming, Bulletin of the Australian Mathematical Society39 (1989), 287–299.

    MATH  MathSciNet  Google Scholar 

  9. M. A. Hanson,On sufficiency of the Kuhn-Tucker conditions, Journal of Mathematical Analysis and Applications80 (1981), 545–550.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Giorgi and E. Molho,Generalized invexity: Relationship with generalized convexity and applications to optimality and duality conditions, In Generalized Concavity for Economic, (Edited by P. Mazzoleni), Tecnoprint, Bologna, (1992), 53–70.

    Google Scholar 

  11. G. Giorgi and S. Mititelu,Convexités généralisées et propriétés, Rev. Roumaine Math. Pures Appl38 (1993), 125–172.

    MATH  MathSciNet  Google Scholar 

  12. G. Giorgi and A. Guerraggio,Various types of nonsmooth invex functions, J. Inform. Optim. Sci17 (1996), 137–150.

    MATH  MathSciNet  Google Scholar 

  13. P. Kanniappan and P. Pandian,On generalized convex functions in optimization theory-A survey, Opsearch33 (1996), 174–185.

    MathSciNet  Google Scholar 

  14. R. Pini and C. Singh,A survey of recent [1985–1995] advances in generalized convexity with applications to duality theory and optimality conditions, Optimization39 (1997), 311–360.

    Article  MATH  MathSciNet  Google Scholar 

  15. G. Giorgi and A. Guerraggio,The notion of invexity in vector optimization: Smooth and nonsmooth cases, In Generalized Convexity, Generalized Monotonicity: Recent Results, (Edited by J. P. Crouzeix et al.), Kluwer Academic, The Netherlands, (1998), 389–405.

    Google Scholar 

  16. M. A. Hanson and B. Mond,Further generalization of convexity in mathematical programming, J. Inform. Optim. Sci3 (1982), 25–32.

    MATH  MathSciNet  Google Scholar 

  17. T. Maeda,Constraint qualifications in multiobjective optimization problems: differentiable case, Journal of Optimization Theory and Applications80 (1994), 483–500.

    Article  MATH  MathSciNet  Google Scholar 

  18. V. Pareto,Cours de Economie Politique, Rouge, Lausanne, Switzerland, 1986.

    Google Scholar 

  19. V. Preda,On efficiency and duality for multiobjective programs, Journal of Mathematical Analysis and Applications166 (1992), 365–377.

    Article  MATH  MathSciNet  Google Scholar 

  20. Z. A. Liang, H. X. Huang and P. M. Pardalos,Efficiency conditions and duality for a class of multiobjective fractional programming problems, Journal of Global Optimization27 (2003), 447–471.

    Article  MATH  MathSciNet  Google Scholar 

  21. T. Tanino and Y. Sawaragi,Duality theory in multiobjective programming, Journal of Optimization Theory and Applications27 (1979), 509–529.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, 116023, Dalian, P. R. China

    Sanming Liu & Enmin Feng

  2. Department of Mathematics, East China Shipbuilding Institute, 212003, Zhen Jiang, P. R. China

    Sanming Liu

Authors
  1. Sanming Liu
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  2. Enmin Feng
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Corresponding author

Correspondence to Enmin Feng.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No. 19871009.

Sanming Liu received her MSc from Jilin University of Technology in 1989 and now is a doctorate student under the direction of Prof. Enmin Feng in Dalian University of Technology, at the meantime she is an associate professor at East China Shipbuilding Institute. Her research interests cover multiobjective programming, theory and application of optimization.

Enmin Feng is a professor and Ph. D. Advisor in Dalian University of Technology. His research interests center on control theory and optimization.

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Liu, S., Feng, E. Another approach to multiobjective programming problems withF-convex functions. JAMC 17, 379–390 (2005). https://doi.org/10.1007/BF02936063

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  • DOI: https://doi.org/10.1007/BF02936063

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