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Multiobjective program with support functions under (G, C, ρ)-convexity assumptions

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Abstract

This paper deals with multiobjective programming problems with support functions under (G, C, ρ)-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of (G, C, ρ)-convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.

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References

  1. Soleimani-damaneh M, On some multiobjective optimization problems arising in biology, International Journal of Computer Mathematics, 2011, 88: 1103–1119.

    Article  MathSciNet  MATH  Google Scholar 

  2. Soleimani-damaneh M, An optimization modelling for string selection in molecular biology using Pareto optimality, Applied Mathematical Modelling, 2011, 35: 3887–3892.

    Article  MathSciNet  MATH  Google Scholar 

  3. Handl J, Kell D, and Knowles J, Multiobjective optimization in bioinformatics and computational biology, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2007, 4: 279–292.

    Article  Google Scholar 

  4. Hakanen J, Miettinen K, and Sahlstedt K, Wastewater treatment: New insight provided by interactive multiobjective optimization, Decision Support Systems, 2011, 51: 328–337.

    Article  Google Scholar 

  5. Abakarov A, Sushkov Y, and Sunpson R, Multiobjective optimization approach: Thermal food processing, Journal of Food Science, 2009, 74(9): E471–E487.

    Google Scholar 

  6. Ekins S, Honeycutt J, and Metz J, Evolving molecules using multi-objective optimization: Applying to ADME/Tox, Drug Discovery Today, 2010, 15(11–12): 451–460.

    Article  Google Scholar 

  7. Chandra S, Craven B, and Mond B, Generalized concavity and duality with a square root term, Optimization, 1985, 16(5): 653–662.

    Article  MathSciNet  MATH  Google Scholar 

  8. Chandra S and Husain I, Symmetric dual nondifferentiable programs, Bulletin of the Australian Mathematical Society, 1981, 24(2): 295–307.

    Article  MathSciNet  MATH  Google Scholar 

  9. Mond B and Schechter M, Nondifferentiable symmetric duality, Bulletin of the Australian Mathematical Society, 1996, 53(2): 177–188.

    Article  MathSciNet  MATH  Google Scholar 

  10. Kim S, Kim M, and Kim D, Optimality and duality for a class of nondifferentiable multiobjective fractional programming problems, Journal of Optimization Theory and Applications, 2006, 129(1): 131–146.

    Article  MathSciNet  MATH  Google Scholar 

  11. Kim D and Bae K, Optimality conditions and duality for a class of nondifferentiable multiobjective programming problems, Taiwanese Journal of Mathematics, 2009, 13(2B): 789–804.

    MathSciNet  MATH  Google Scholar 

  12. Sang K and Jung L, Optimality conditions and duality in nonsmooth multiobjective programs, Journal of Inequalities and Applications, 2010, 2010: Article ID 939537.

  13. Bae K, Kang Y, and Kim D, Efficiency and generalized convex duality for nondifferentiable multiobjective programs, Journal of Inequalities and Applications, 2010, 2010: Article ID 930457.

  14. Bae K and Kim D, Optimality and duality theorems in nonsmooth multiobjective optimization, Fixed Point Theory and Applications, 2011, 2011(42): 1–11.

    MathSciNet  Google Scholar 

  15. Liang Z, Huang H, and Pardalos P, Optimality conditions and duality for a class of nonlinear fractional programming problems, Journal of Optimization Theory and Applications, 2001, 110(3): 611–619.

    Article  MathSciNet  MATH  Google Scholar 

  16. Liang Z, Huang H, and Pardalos P, Efficiency conditions and duality for a class of multiobjective fractional programming problems, Journal of Global Optimization, 2003, 27(4): 447–471.

    Article  MathSciNet  MATH  Google Scholar 

  17. Preda V, On sufficiency and duality for multiobjective programs, Journal of Mathematical Analysis and Applications, 1992, 166(2): 365–377.

    Article  MathSciNet  MATH  Google Scholar 

  18. Bhatia D and Jain P, Generalized (F, ρ)-convexity and duality for nonsmooth multiobjective programs, Optimization, 1994, 31(2): 153–164.

    Article  MATH  Google Scholar 

  19. Yuan D, Liu X, Chinchuluun A, and Pardalos P, Nondifferentiable minimax fractional programming problems with (C, a, α, d)-convexity, Journal of Optimization Theory and Applications, 2006, 129(1): 185–199.

    Article  MathSciNet  MATH  Google Scholar 

  20. Chinchuluun A, Yuan D, and Pardalos P, Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity, Annals of Operations Research, 2007, 154(1): 133–147.

    Article  MathSciNet  MATH  Google Scholar 

  21. Long X, Optimality conditions and duality for nondifferentiable multiobjective fractional programming problems with (C, α, a, d)-convexity, Journal of Optimization Theory and Applications, 2011, 148(1): 197–208.

    Article  MathSciNet  MATH  Google Scholar 

  22. Soleimani-Damaneh M, Nonsmooth optimization using Mordukhovich’s subdifferential, SIAM Journal on Control and Optimization, 2010, 48(5): 3403–3436.

    Article  MathSciNet  MATH  Google Scholar 

  23. Soleimani-Damaneh M, Characterizations and applications of generalized invexity and monotonicity in Asplund spaces, TOP, 2012, 20(3): 592–613.

    Article  MathSciNet  MATH  Google Scholar 

  24. Soleimani-damaneh M, Optimality and invexity in optimization problems in Banach algebras (spaces), Nonlinear Analysis: Theory, Methods and Applications, 2009, 71(11): 5522–5530.

    Article  MathSciNet  MATH  Google Scholar 

  25. Soleimani-Damaneh M, Multiple-objective programs in Banach spaces: Sufficiency for (proper) optimality, Nonlinear Analysis: Theory, Methods and Applications, 2007, 67(3): 958–962.

    Article  MathSciNet  MATH  Google Scholar 

  26. Soleimani-Damaneh M, Duality for optimization problems in Banach algebras, Journal of Global Optimization, 2012, 54(2): 375–388.

    Article  MathSciNet  MATH  Google Scholar 

  27. Antczak T, New optimality conditions and duality results of G-type in differentiable mathematical programming, Nonlinear Analysis: Theory, Methods and Applications, 2007, 66(7): 1617–1632.

    Article  MathSciNet  MATH  Google Scholar 

  28. Antczak T, On G-invex multiobjective programming. Part I. Optimality, Journal of Global Optimization, 2009, 43(1): 97–109.

    Article  MathSciNet  MATH  Google Scholar 

  29. Antczak T, On G-invex multiobjective programming. Part II. Duality, Journal of Global Optimization, 2009, 43(1): 111–140.

    Article  MathSciNet  MATH  Google Scholar 

  30. Yuan D, Liu X, Yang S, and Lai G, Multiobjective programming problems with (G, C, ρ)- convexity, Journal of Applied Mathematics and Computing, 2012, 40(1–2): 383–397.

    Article  MathSciNet  MATH  Google Scholar 

  31. Yang X, Teo K, and Yang X, Duality for a class of nondifferentiable multiobjective programming problems, Journal of Mathematical Analysis and Applications, 2000, 252(2): 999–1005.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Hanshan Normal University, Chaozhou, 521041, China

    Dehui Yuan & Xiaoling Liu

Authors
  1. Dehui Yuan
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  2. Xiaoling Liu
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Corresponding author

Correspondence to Dehui Yuan.

Additional information

This research was supported by the Natural Science Foundation of Guangdong Province under Grant No. S2013010013101 and the Science Foundations of Hanshan Normal University under Grant Nos. QD20131101 and LZ201403.

This paper was recommended for publication by Editor WANG Shouyang.

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Yuan, D., Liu, X. Multiobjective program with support functions under (G, C, ρ)-convexity assumptions. J Syst Sci Complex 28, 1148–1163 (2015). https://doi.org/10.1007/s11424-015-2249-7

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  • DOI: https://doi.org/10.1007/s11424-015-2249-7

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