IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v135y2007i3d10.1007_s10957-007-9271-4.html
   My bibliography  Save this article

Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions

Author

Listed:
  • T. R. Gulati

    (Indian Institute of Technology)

  • I. Ahmad

    (Aligarh Muslim University)

  • D. Agarwal

    (Indian Institute of Technology)

Abstract

In this paper, new classes of generalized (F,α,ρ,d)-V-type I functions are introduced for differentiable multiobjective programming problems. Based upon these generalized convex functions, sufficient optimality conditions are established. Weak, strong and strict converse duality theorems are also derived for Wolfe and Mond-Weir type multiobjective dual programs.

Suggested Citation

  • T. R. Gulati & I. Ahmad & D. Agarwal, 2007. "Sufficiency and Duality in Multiobjective Programming under Generalized Type I Functions," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 411-427, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9271-4
    DOI: 10.1007/s10957-007-9271-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-007-9271-4
    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/s10957-007-9271-4?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. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    2. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Sorger, Gerhard, 2004. "Consistent planning under quasi-geometric discounting," Journal of Economic Theory, Elsevier, vol. 118(1), pages 118-129, September.
    2. Huynh Ngai & Nguyen Huu Tron & Nguyen Vu & Michel Théra, 2022. "Variational Analysis of Paraconvex Multifunctions," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 180-218, June.
    3. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.
    4. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    5. S. Nobakhtian, 2006. "Sufficiency in Nonsmooth Multiobjective Programming Involving Generalized (Fρ)-convexity," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 361-367, August.
    6. Sorger, Gerhard, 1995. "On the sensitivity of optimal growth paths," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 353-369.
    7. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
    8. Sedi Bartz & Minh N. Dao & Hung M. Phan, 2022. "Conical averagedness and convergence analysis of fixed point algorithms," Journal of Global Optimization, Springer, vol. 82(2), pages 351-373, February.
    9. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    10. Hugo Leiva & Nelson Merentes & Kazimierz Nikodem & José Sánchez, 2013. "Strongly convex set-valued maps," Journal of Global Optimization, Springer, vol. 57(3), pages 695-705, November.
    11. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    12. Venditti Alain, 2019. "Competitive equilibrium cycles for small discounting in discrete-time two-sector optimal growth models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-14, September.
    13. Anurag Jayswal & Vivek Singh & Krishna Kummari, 2017. "Duality for nondifferentiable minimax fractional programming problem involving higher order $$(\varvec{C},\varvec{\alpha}, \varvec{\rho}, \varvec{d})$$ ( C , α , ρ , d ) -convexity," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 598-617, September.
    14. Albert Ferrer & Adil Bagirov & Gleb Beliakov, 2015. "Solving DC programs using the cutting angle method," Journal of Global Optimization, Springer, vol. 61(1), pages 71-89, January.
    15. Francisco Facchinei & Jong-Shi Pang & Gesualdo Scutari, 2014. "Non-cooperative games with minmax objectives," Computational Optimization and Applications, Springer, vol. 59(1), pages 85-112, October.
    16. Phan Tu Vuong & Jean Jacques Strodiot, 2018. "The Glowinski–Le Tallec splitting method revisited in the framework of equilibrium problems in Hilbert spaces," Journal of Global Optimization, Springer, vol. 70(2), pages 477-495, February.
    17. Giancarlo Bigi & Mauro Passacantando, 2017. "Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 63-79, November.
    18. David Barilla & Giuseppe Caristi & Nader Kanzi, 2022. "Optimality and duality in nonsmooth semi-infinite optimization, using a weak constraint qualification," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 503-519, December.
    19. F. Lara, 2022. "On Strongly Quasiconvex Functions: Existence Results and Proximal Point Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 891-911, March.
    20. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.

    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:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9271-4. 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.