Skip to main content
Log in

η-Pseudolinearity

η-Pseudolinearità

  • Articles
  • Published:
Rivista di matematica per le scienze economiche e sociali Aims and scope Submit manuscript

Abstract

The notion of η-pseudolinearity is introduced. First, some characterizations of an η-pseudolinear function are obtained. Then characterizations of the solution set of an η-pseudolinear program are derived. The paper generalizes various results on pseudolinear functions and programs.

Riassunto

Il lavoro introduce la nozione di η-pseudolinearità. Dopo avere ottenuto alcune caratterizzazioni delle funzioni η-pseudolineari, si derivano caratterizzazioni dell'insieme delle soluzioni di un programma η-pseudolineare. Lo studio generalizza diversi risultati sulle funzioni e sui programmi pseudolineari.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Avriel M., Diewert W. E., Schaible S., Zang I.,Generalized Concavity, Plenum Press, New York and London, 1988.

    Book  Google Scholar 

  2. Ben-Israel A., Mond B.,What is Invexity?, Journal of the Australian Mathematical Society, 1986, Series B. 28, 1–9.

    Article  Google Scholar 

  3. Cambini R.,Funzioni Scalari Affini Generalizzate, Rivista di Matematica per le Scienze Economiche e Sociali, 18(2), 1995, 153–163.

    Article  Google Scholar 

  4. Chew K. L., Choo E. U.,Pseudolincarity and Efficiency, Mathematical Programming, 28, 1984, 226–239.

    Article  Google Scholar 

  5. Craven B. D.,Duality for Generalized Convex Fractional Programs, inGeneralized Concavity in Optimization and Economics, (eds. S. Schaible and W. T. Ziemba), Academic Press, New York, 1981a, 473–489.

    Google Scholar 

  6. Craven B. D.,Invex Functions and Constrained Local Minima, Bulletin of the Australian Mathematical Society, 24, 1981b, 357–366.

    Article  Google Scholar 

  7. Hanson M. A.,On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, 80, 1981, 545–550.

    Article  Google Scholar 

  8. Jeyakumar V., Yang X. Q.,On Characterizing the Solution Sets of Pseudolinear Programs, Journal of Optimization Theory and Applications, 87, 1995, 747–755.

    Article  Google Scholar 

  9. Kaul R. N., Kaur S.,Optimality Criteria in Nonlinear Programming involving Nonconvex Functions, Journal of Mathematical Analysis and Applications, 105, 1985, 104–112.

    Article  Google Scholar 

  10. Komlósi S.,First and Second Order Characterizations of Pseudolinear Functions, European Journal of Operational Research, 67, 1993, 278–286.

    Article  Google Scholar 

  11. Kortanek K. O., Evans J. P.,Pseudoconcave Programming and Lagrange Regularity, Operations Research, 15, 1967, 882–892.

    Article  Google Scholar 

  12. Mangasarian O. L.,Pseudo-convex Functions, SIAM Journal of Control, 3, 1965, 281–290.

    Google Scholar 

  13. Martos B. Nonlinear Programming: Theory and Methods, North-Holland, Amsterdam, 1975.

    Google Scholar 

  14. Mohan S. R., Neogy S. K. On Invex Sets and Preinvex Functions, Journal of Mathematical Analysis and Applications, 189, 1994, 901–908.

    Article  Google Scholar 

  15. Weir T., Mond B.,Pre-invex Functions in Multiple Objective Optimization, Journal of Mathematical Analysis and Applications, 136, 1988, 29–38.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Siegfried Schaible.

Additional information

This research was supported by the National Science Council of the Republic of China. We are grateful for helpful comments from Professor E. Molho and two anonymous referees.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ansari, Q.H., Schaible, S. & Yao, JC. η-Pseudolinearity. Decisions Econ Finan 22, 31–39 (1999). https://doi.org/10.1007/BF02912349

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02912349

Keywords

1991 MS Classification

Navigation