IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v16y2016i2d10.1007_s12351-015-0206-9.html
   My bibliography  Save this article

Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints

Author

Listed:
  • Hachem Slimani

    (University of Bejaia)

  • Mohammed-Said Radjef

    (University of Bejaia)

Abstract

In this paper, we study Fritz John type optimality conditions for constrained nonlinear programming in which equality and inequality constraints are together present. We introduce a generalized Fritz John condition which is necessary and sufficient for a feasible point to be an optimal solution under weak invexity. In particular, by combining the introduced generalized Fritz John condition with the invexity with respect to different functions, we obtain sufficient optimality conditions which extend and generalize various results in the literature, and their importance and usefulness are illustrated on examples .

Suggested Citation

  • Hachem Slimani & Mohammed-Said Radjef, 2016. "Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints," Operational Research, Springer, vol. 16(2), pages 349-364, July.
    • Handle: RePEc:spr:operea:v:16:y:2016:i:2:d:10.1007_s12351-015-0206-9
    DOI: 10.1007/s12351-015-0206-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-015-0206-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12351-015-0206-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stancu-Minasian, I.M., 2006. "Optimality and duality in nonlinear programming involving semilocally B-preinvex and related functions," European Journal of Operational Research, Elsevier, vol. 173(1), pages 47-58, August.
    2. Bhatia, D. & Sharma, A., 2003. "New-invexity type conditions with applications to constrained dynamic games," European Journal of Operational Research, Elsevier, vol. 148(1), pages 48-55, July.
    3. Suneja, S.K. & Khurana, Seema & Vani, 2008. "Generalized nonsmooth invexity over cones in vector optimization," European Journal of Operational Research, Elsevier, vol. 186(1), pages 28-40, April.
    4. J.M. Martínez & B.F. Svaiter, 2003. "A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 117-133, July.
    5. Slimani, Hachem & Radjef, Mohammed Said, 2010. "Nondifferentiable multiobjective programming under generalized dI-invexity," European Journal of Operational Research, Elsevier, vol. 202(1), pages 32-41, April.
    6. R. Zeng & R. J. Caron, 2006. "Generalized Motzkin Theorems of the Alternative and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 281-299, November.
    7. Hachem Slimani & Shashi Kant Mishra, 2014. "Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-12, May.
    8. Birbil, S.I. & Frenk, J.B.G. & Still, G.J., 2007. "An elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 479-484, July.
    9. T. Antczak, 2005. "Modified Ratio Objective Approach in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 23-40, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Slimani, Hachem & Radjef, Mohammed Said, 2010. "Nondifferentiable multiobjective programming under generalized dI-invexity," European Journal of Operational Research, Elsevier, vol. 202(1), pages 32-41, April.
    2. Roberto Andreani & José Mario Martínez & Alberto Ramos & Paulo J. S. Silva, 2018. "Strict Constraint Qualifications and Sequential Optimality Conditions for Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 43(3), pages 693-717, August.
    3. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    4. R. Gárciga Otero & B. F. Svaiter, 2008. "New Condition Characterizing the Solutions of Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 89-98, April.
    5. Tadeusz Antczak, 2023. "On directionally differentiable multiobjective programming problems with vanishing constraints," Annals of Operations Research, Springer, vol. 328(2), pages 1181-1212, September.
    6. Ariana Pitea & Mihai Postolache, 2012. "Duality theorems for a new class of multitime multiobjective variational problems," Journal of Global Optimization, Springer, vol. 54(1), pages 47-58, September.
    7. A. Pascoletti & P. Serafini, 2007. "Differential Conditions for Constrained Nonlinear Programming via Pareto Optimization," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 399-411, September.
    8. Hachem Slimani & Shashi Kant Mishra, 2014. "Multiobjective Fractional Programming Involving Generalized Semilocally V-Type I-Preinvex and Related Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-12, May.
    9. Renan W. Prado & Sandra A. Santos & Lucas E. A. Simões, 2023. "On the Fulfillment of the Complementary Approximate Karush–Kuhn–Tucker Conditions and Algorithmic Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 705-736, May.
    10. R. Andreani & S. Castro & J. Chela & A. Friedlander & S. Santos, 2009. "An inexact-restoration method for nonlinear bilevel programming problems," Computational Optimization and Applications, Springer, vol. 43(3), pages 307-328, July.
    11. Juliano Francisco & J. Martínez & Leandro Martínez & Feodor Pisnitchenko, 2011. "Inexact restoration method for minimization problems arising in electronic structure calculations," Computational Optimization and Applications, Springer, vol. 50(3), pages 555-590, December.
    12. Surjeet Kaur Suneja & Sunila Sharma & Mamta Chaudhary, 2018. "Vector optimization with generalized cone locally connected functions," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 302-319, June.
    13. Ademir A. Ribeiro & Mael Sachine & Evelin H. M. Krulikovski, 2022. "A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 1067-1083, March.
    14. Fulga, C. & Preda, V., 2009. "Nonlinear programming with E-preinvex and local E-preinvex functions," European Journal of Operational Research, Elsevier, vol. 192(3), pages 737-743, February.
    15. Gabriel Haeser & María Laura Schuverdt, 2011. "On Approximate KKT Condition and its Extension to Continuous Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 528-539, June.
    16. J. Li & G. Mastroeni, 2016. "Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 91-115, April.
    17. Brinkhuis, Jan, 2009. "A linear programming proof of the second order conditions of non-linear programming," European Journal of Operational Research, Elsevier, vol. 192(3), pages 1001-1007, February.
    18. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2014. "Some Notes on Approximate Optimality Conditions in Scalar and Vector Optimization Problems," DEM Working Papers Series 095, University of Pavia, Department of Economics and Management.
    19. Li Tang & Ke Zhao, 2013. "Optimality conditions for a class of composite multiobjective nonsmooth optimization problems," Journal of Global Optimization, Springer, vol. 57(2), pages 399-414, October.
    20. M. Arana-Jiménez & G. Ruiz-Garzón & R. Osuna-Gómez & B. Hernández-Jiménez, 2013. "Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 266-277, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:operea:v:16:y:2016:i:2:d:10.1007_s12351-015-0206-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.