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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2014 / Cilt: 4 - Sayı: 1

A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization

Hehua JİAO
Pages
1–10
Publication Date
2022-10-11
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, as its applications, some optimality conditionsand duality results are established for a nondifferentiable vector optimization under the aforesaid mapsassumptions

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces isintroduced for a nondifferentiable vector optimization problem with restrictions of inequalities andsome of its basic properties are studied.
📊
Key Findings & Data:In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces isintroduced for a nondifferentiable vector optimization problem with restrictions of inequalities andsome of its basic properties are studied.
💡
Conclusion & Impact:Furthermore, as its applications, some optimality conditionsand duality results are established for a nondifferentiable vector optimization under the aforesaid mapsassumptions
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, a new class of semilocal E-preinvex and related maps in Banach spaces isintroduced for a nondifferentiable vector optimization problem with restrictions of inequalities andsome of its basic properties are studied. Furthermore, as its applications, some optimality conditionsand duality results are established for a nondifferentiable vector optimization under the aforesaid mapsassumptions

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Cite This Article

JİAO, H. (2022). A class of semilocal E-preinvex maps in Banach spaces with applications to nondifferentiable vector optimization. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 4 - Sayı: 1, 1–10. https://ajindex.com/articles/440725

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References (16)

  1. Hanson, M.A. and Mond, B., Necessary and sufficient conditions in constrained optimization. Math. Program., 37, 51-58 (1987)
  2. Kaul, R.N., Suneja, S.K., Srivastava, M.K., Optimality criteria and duality in multiple objective optimization involving generalized invexity. J. Optim. Theory Appl., 80, 465-482 (1994)
  3. Rueda, N.G. and Hanson, M.A., Optimality criteria in mathematical programming involving generalized invexity. J. Math. Anal. Appl., 130, 375-385 (1998)
  4. Mukherjee, R.N. and Mishra, S.K., Multiobjective programming with semilocally convex functions. J. Math. Anal. Appl., 199, 409-424 (1996)
  5. Hachimi, M. and Aghezzaf, B., Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions. J. Math. Anal. Appl., 319, 110- 123 (2006)
  6. Mishra, S.K. and Noor, M.A., Some nondifferentiable multi-objective programming problems. J. Math. Anal. Appl., 316, 472-482 (2006)
  7. Preda, V. and Stancu-Minasian, I.M., Duality in multiple objective programming involving semilocally preinvex and related functions. Glas. Mat. Ser. Ill., 32, 153-165 (1997)
  8. Preda, V., Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions. J. Math. Anal. Appl., 288, 365-382 (2003)
  9. Batista dos Santos, L., Osuna-G´omez, R., Rojas-Medar, M.A., Rufi´an-Lizana, A., Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces. Comput. Math. Appl., 48, 885-895 (2004)
  10. Yu, G.L. and Liu, S.Y., Some vector optimization problems in Banach spaces with generalized convexity. Comput. Math. Appl., 54, 1403-1410 (2007)
  11. Chen, X.S., Some properties of semi-Econvex functions. J. Math. Anal. Appl., 275, 251-262 (2002)
  12. Hu, Q.J., Jian, J.B., Zheng, H.Y., Tang, C.M., Semilocal E-convexity and semilocal E-convex programming. Bull. Aust. Math. Soc., 75, 59-74 (2007)
  13. Fulga, C., Preda, V., Nonlinear programming with E-preinvex and local E-preinvex functions. Eur. J. Oper. Res., 192, 737-743 (2009)
  14. Luo, Z.M. and Jian, J.B., Some properties of semi-E-preinvex maps in Banach spaces. Nonlinear Anal: Real World Appl., 12, 1243- 1249 (2011)
  15. Craven, B.D., Control and Optimization. Chapman and Hall, London, (1995)
  16. Niculescu, C., Optimality and duality in multiobjective fractional programming involving ρ-semilocally type I-preinvex and related functions. J. Math. Anal. Appl., 335, 7-19 (2007).