Skip to main content

Recent Developments in Second Order Necessary Optimality Conditions

  • Chapter

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 27))

Abstract

In this paper a new second order necessary optimality condition, stated in the so-called image space, is established; such a condition allows to obtain, as particular cases, some recent results which are presented in order to stimulate and improve the study in second order optimality conditions.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben-Tal A., “Second-order and related extremelity conditions in nonlinear programming”, Journal of Optimization Theory and Applications, vol. 31, n. 2, pp. 143–165, 1980.

    Article  MathSciNet  Google Scholar 

  2. Cambini A. and L. Martein, “Generalized concavity and optimality conditions in vector and scalar optimization”, in Generalized Convexity, edited by Komlósi S., Rapcsák T. and S. Schaible, Springer-Verlag, Heidelberg, pp. 337–357, 1994.

    Google Scholar 

  3. Cambini A. and L. Martein, “Second order necessary optimality conditions in the image space: preliminary results”, in Scalar and Vector Optimization in Economic and Financial Problems, edited by Castagnoli E. and G. Giorgi, pp. 27–38, 1995.

    Google Scholar 

  4. Cambini A., Martein L. and R. Cambini, “A new approach to second order optimality conditions in vector optimization”, Technical Report n.103, Dept. of Statistics and Applied Mathematics, University of Pisa, 1996. A revised version will appear in the Proceedings of the Second International Conference in Multi-objective Programming and Goal Programming, Torremolinos (Spain ), 1996.

    Google Scholar 

  5. Cambini R., “Second order optimality conditions in multiobjective programming”, to appear in the journal Optimization.

    Google Scholar 

  6. Cambini, R., “Generalized Concavity and Optimality Conditions in Vector Optimization”, in Operations Research and its Applications, Proceedings of the 2nd International Symposium on Operations Research with Applications in Engineering, Technology and Management (ISORA96), held in Guilin (P.R. China), 11th–14th of December, 1996, edited by D.Z. Du, X.S. Zhang and K. Cheng, World Publishing Corporation, Beijing, pp. 172–180, 1996.

    Google Scholar 

  7. Kawasaki H., “Second-order necessary conditions of the Kuhn-Tucker type under new constraint qualifications”, Journal of Optimization Theory and Applications, vol. 57, n. 2, 1988.

    Google Scholar 

  8. McCormick G.P, “Second order conditions for constrained minima”, SIAM Journal of Applied Mathematics, vol. 15, n. 3, pp. 641–652, 1967.

    Article  MathSciNet  MATH  Google Scholar 

  9. Penot J.P, “Optimality conditions in mathematical programming and composite optimization”, Mathematical Programming, vol. 67, pp. 225–245, 1994.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Kluwer Academic Publishers. Printed in the Netherlands

About this chapter

Cite this chapter

Cambini, A., Komlósi, S., Martein, L. (1998). Recent Developments in Second Order Necessary Optimality Conditions. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3341-8_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3343-2

  • Online ISBN: 978-1-4613-3341-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics