Skip to main content

Advertisement

SpringerLink
Log in

Barrier method in nonsmooth convex optimization without convex representation

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In this article we want to demonstrate that under mild conditions the barrier method is an effective solution approach for convex optimization problems whose objective is nonsmooth and whose feasible set is described by smooth inequality constraints in which all the constraint functions need not be convex.

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

  1. Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming, Theory and Algorithms, 3rd edn. Wiley, New York (2006)

    Book  MATH  Google Scholar 

  2. Borwein, J.M., Lewis, A.S.: Convex Analysis and Nonlinear Optimization, 2nd edn. Springer, Berlin (2006)

    Book  MATH  Google Scholar 

  3. Clake, F.H.: Generalized gradients and applications. Trans. Am. Math. Soc. 205, 247–262 (1975)

    Article  Google Scholar 

  4. Clarke, F.H.: Optimization and Nonsmooth Analysis. Wiley Interscience, New York (1983)

    MATH  Google Scholar 

  5. Dutta, J., Lalitha, C.S.: Optimality conditions in convex optimization revisited. Optim. Lett. 7(2), 221–229 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Guler, O.: Foundations of Optimization. Springer, Berlin (2010)

    Book  Google Scholar 

  7. Hiriart-Urruty, J.-B.: Miscellanies on nonsmooth analysis and optimization, in nondifferentiable optimization: motivation and applications. workshop in Sopron, 1984. In: Demyanov, V.F., Pallaschke, D. (eds.) Lecture Notes in Economics and Mathematical Systems, vol.255, pp. 8–24. Springer, Berlin (1985)

  8. Lasserre, J.B.: On representations of the feasible set in convex optimization. Optim. Lett. 4(1), 1–5 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lasserre, J.B.: On convex optimization without convex representation. Optim. Lett. 5(4), 549–556 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lasserre, J.B.: Erratum to: On convex optimization without convex representation. Optim. Lett. 8(5), 1795–1796 (2014)

    Article  MathSciNet  Google Scholar 

  11. Rockafellar, R.T.: Convex Analysis. Princeton, New Jersey (1970)

    MATH  Google Scholar 

Download references

Acknowledgments

We would like to convey our thanks to the two anonymous referees whose constructive comments have improved the presentation of the paper.

Author information

Authors and Affiliations

  1. Economics Group, Department of Humanities and Social Sciences, Indian Institute of Technology, Kanpur, 208016, India

    Joydeep Dutta

Authors
  1. Joydeep Dutta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joydeep Dutta.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dutta, J. Barrier method in nonsmooth convex optimization without convex representation. Optim Lett 9, 1177–1185 (2015). https://doi.org/10.1007/s11590-014-0811-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-014-0811-1

Keywords

Search

Navigation