Skip to main content
SpringerLink
Log in

Generalized Concavity in Multi-objective Optimization

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords

Efficiency

Optimality Conditions

F. John Generalized Conditions

Connectedness of the Efficient Points Sets

See also

References

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Arrow KJ, Enthoven AC (1961) Quasi-concave programming. Econometrica 29:779–800

    Article  MathSciNet  MATH  Google Scholar 

  2. Cambini A, Martein L (1993) An approach to optimality conditions in vector and scalar optimization. In: Diewert WE et al (eds) Mathematical modelling in Economics. Springer, Berlin, pp 345–358

    Google Scholar 

  3. Cambini A, Martein L (1994) Generalized concavity and optimality conditions in vector and scalar optimization. In: Komlosi S, Rapcsak T, Schaible S (eds) Generalized Convexity. vol. Lecture Notes Economics and Math Systems. Springer, Berlin, pp 337–357

    Google Scholar 

  4. Cambini A, Martein L (1998) Generalized concavity in multiobjective programming. In: Crouzeix JP, Martinez-Legaz JE, Volle M (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Kluwer, Dordrecht, pp 453–467

    Google Scholar 

  5. Cambini A, Martein L, Cambini R (1997) Some optimality conditions in multiobjective programming. In: Climaco JN (ed) Multicriteria Analysis. Springer, Berlin, pp 168–178

    Google Scholar 

  6. Cambini R (1996) Generalized concavity and optimality conditions in vector optimization. In: Du D-Z, Zhang X-S, Cheng K (eds) Oper. Res. Appl. World Publ. Corp., pp 172–180

    Google Scholar 

  7. Cambini R (1996) Some new classes of generalized concave vector-valued functions. Optim 36:11–24

    Article  MathSciNet  MATH  Google Scholar 

  8. Cambini R (1998) Generalized concavity for bicriteria functions. In: Crouzeix JP, Martinez-Legaz JE, Volle M (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Kluwer, Dordrecht, pp 439–451

    Google Scholar 

  9. Daniilidis A, Hadjisavvas N, Schaible S (1997) Connectedness of the efficient set for three- objective quasiconcave maximization problems. J Optim Th Appl 93(3):517–524

    Article  MathSciNet  MATH  Google Scholar 

  10. Jahn J (1986) Mathematical vector optimization in partially ordered linear spaces. P. Lang, Frankfurt am Main

    MATH  Google Scholar 

  11. Jahn J, Sach E (1986) Generalized quasiconvex mappings and vector optimization. SIAM J Control Optim 24(2):306–322

    Article  MathSciNet  MATH  Google Scholar 

  12. Luc DT (1987) Connectedness of the efficient point sets in quasiconcave vector maximization. J Math Anal Appl 122:346–354

    Article  MathSciNet  MATH  Google Scholar 

  13. Luc DT (1988) Theory of vector optimization. Lecture Notes Economics and Math Systems, vol 319. Springer, Berlin

    MATH  Google Scholar 

  14. Mangasarian OL (1969) Nonlinear programming. McGraw-Hill, New York

    MATH  Google Scholar 

  15. Schaible S (1983) Bicriteria quasiconcave programs. Cahiers CERO 25:93–101

    MathSciNet  MATH  Google Scholar 

  16. Warburton AR (1983) Quasiconcave vector maximization: connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives. J Optim Th Appl 40(4):537–557

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Statistics and Applied Math., University Pisa, Pisa, Italy

    Alberto Cambini & Laura Martein

Authors
  1. Alberto Cambini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laura Martein
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, NJ, 08544-5263, USA

    Christodoulos A. Floudas

  2. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Cambini, A., Martein, L. (2008). Generalized Concavity in Multi-objective Optimization . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_202

Download citation

Publish with us

Policies and ethics

Search

Navigation