Skip to main content
SpringerLink
Log in

Generalized (η,ρ)-Invex Functions and Global Semiparametric Sufficient Efficiency Conditions for Multiobjective Fractional Programming Problems Containing Arbitrary Norms

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

The purpose of this paper is to develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (η, ρ)-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ben-Israel A. and Mond B. (1986). What is invexity?. Journal of the Australian Mathematical Society Series B. 28: 1–9

    Google Scholar 

  • Craven B.D. (1981). Invex functions and constrained local minima. Bulletin of the Australian Mathematical Society 24: 357–366

    Google Scholar 

  • Giorgi G. and Guerraggio A. (1996). Various types of nonsmooth invex functions. Journal of Information and Optimization Sciences 17: 137–150

    Google Scholar 

  • Giorgi G. and Mititelu S. (1993). Convexités généralisées et propriétés. Revue Roumaine des Mathématiques Pures et Appliquées 38: 125–172

    Google Scholar 

  • Hanson M.A. (1981). On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 80: 545–550

    Article  Google Scholar 

  • Hanson M.A. and Mond B. (1982). Further generalizations of convexity in mathematical programming. Journal of Information and Optimization Sciences 3: 25–32

    Google Scholar 

  • Horn R.A. and Johnson C.R. (1985). Matrix Analysis. Cambridge University Press, New York

    Google Scholar 

  • Jeyakumar V. (1985). Strong and weak invexity in mathematical programming. Methods of Operations Research 55: 109–125

    Google Scholar 

  • Kanniappan P. and Pandian P. (1996). On generalized convex functions in optimization theory – A survey. Opsearch 33: 174–185

    Google Scholar 

  • Martin D.H. (1985). The essence of invexity. Journal of Optimization Theory and Applications 47: 65–76

    Article  Google Scholar 

  • Miettinen K.M. (1999). Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Mititelu S. and Stancu-Minasian I.M. (1993). Invexity at a point: generalizations and classification. Bulletin of the Australian Mathematical Society 48: 117–126

    Google Scholar 

  • Mond B. and Weir T. (1981). Generalized concavity and duality. In: Schaible, S. and Ziemba, W.T. (eds) Generalized Concavity in Optimization and Economics., pp 263–279. Academic Press, New York

    Google Scholar 

  • Pini R. (1991). Invexity and generalized convexity. Optimization 22: 513–525

    Article  Google Scholar 

  • Pini R. and Singh C. (1997). A survey of recent [1985–1995] advances in generalized convexity with applications to duality theory and optimality conditions. Optimization 39: 311–360

    Article  Google Scholar 

  • Reiland T.W. (1990). Nonsmooth invexity. Bulletin of the Australian Mathematical Society 42: 437–446

    Article  Google Scholar 

  • Sawaragi Y., Nakayama H. and Tanino T. (1986). Theory of Multiobjective Optimization. Academic Press, New York

    Google Scholar 

  • White D.J. (1982). Optimality and Efficiency. Wiley, New York

    Google Scholar 

  • Yang X. (1994). Generalized convex duality for multiobjective fractional programs. Opsearch 31: 155–163

    Google Scholar 

  • Yu P.L. (1985). Multiple-Criteria Decision Making: Concepts, Techniques and Extensions. Plenum Press, New York

    Google Scholar 

  • Zalmai G.J. (1994). Optimality conditions and duality models for a class of nonsmooth constrained fractional variational problems. Optimization 30: 15–51

    Article  Google Scholar 

  • Zalmai G.J. (1996). Continuous-time multiobjective fractional programming. Optimization 37: 1–25

    Article  Google Scholar 

  • Zalmai G.J. (1996). Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, part I: theory. Utilitas Mathematica 50: 163–202

    Google Scholar 

  • Zalmai G.J. (1997). Proper efficiency conditions and duality models for nonsmooth multiobjective fractional programming problems with operator constraints, part II: applications. Utilitas Mathematica 51: 193–237

    Google Scholar 

  • Zalmai G.J. (1998). Proper efficiency principles and duality models for a class of continuous-time multiobjective fractional programming problems with operator constraints. Journal of Statistics and Management Systems 1: 11–59

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Northern Michigan University, 1401 Presque Isle Avenue, Marquette, Michigan, 49855, USA

    G. J. Zalmai

Authors
  1. G. J. Zalmai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. J. Zalmai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zalmai, G.J. Generalized (η,ρ)-Invex Functions and Global Semiparametric Sufficient Efficiency Conditions for Multiobjective Fractional Programming Problems Containing Arbitrary Norms. J Glob Optim 36, 51–85 (2006). https://doi.org/10.1007/s10898-006-6586-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-006-6586-x

Keywords

Keywords

Search

Navigation