Skip to main content
SpringerLink
Log in

Optimality conditions and a barrier method in optimization with convex geometric constraint

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

Abstract

In this note we address a new look to some questions raised by Lasserre in his works (Optim. Lett. 4:1–5, 2010, Optim. Lett. 5:549–556, 2011), concerning the preservation of the conclusions of some results in smooth convex optimization with inequalities constraints to the case where the feasible set is convex, but has no convex representation. The main results we show concern, on one hand, some relations between the hypotheses imposed by Lasserre and the Mangasarian–Fromowitz condition, and, on the other hand, a barrier method based only on the geometric representation of the feasible set.

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. Bonnans, F., Shapiro, A.: Perturbation Analysis of Optimization Problems. Springer, New York (2000)

    Book  MATH  Google Scholar 

  2. Clarke, F.: Functional Analysis, Calculus of Variations and Optimal Control, Graduate Texts in Mathematics, vol. 264. Springer, London (2013)

    Book  Google Scholar 

  3. Dhara, A., Dutta, J.: Optimality Conditions in Convex Optimization. A Finite-Dimensional View. CRC Press, New York (2012)

    MATH  Google Scholar 

  4. Durea, M., Strugariu, R.: An Introduction to Nonlinear Optimization Theory. De Gruyter Open, Warsaw (2014)

    Book  MATH  Google Scholar 

  5. Dutta, J.: Barrier method in nonsmooth convex optimization without convex representation. Optim. Lett. 9, 1177–1185 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Hiriart-Urruty, J.-B.: New concepts in nondifferentiable programming. Mémoires de la SMF 60, 57–85 (1979)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, Vol. I: Basic Theory, Vol. II: Applications, A Series of Comprehensive Studies in Mathematics, vols. 330 and 331. Springer, Berlin (2006)

  12. Zălinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, Singapore (2002)

    Book  MATH  Google Scholar 

Download references

Acknowledgements

The authors thank one of the referees for his/her constructive comments. This work was supported by a grant of Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, project number PN-III-P4-ID-PCE-2016-0188, within PNCDI III.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, “Alexandru Ioan Cuza” University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Marius Durea

  2. “Octav Mayer” Institute of Mathematics of the Romanian Academy, Iaşi, Romania

    Marius Durea

  3. Department of Mathematics, “Gheorghe Asachi” Technical University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Radu Strugariu

Authors
  1. Marius Durea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Radu Strugariu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marius Durea.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Durea, M., Strugariu, R. Optimality conditions and a barrier method in optimization with convex geometric constraint. Optim Lett 12, 923–931 (2018). https://doi.org/10.1007/s11590-018-1232-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-018-1232-3

Keywords

Search

Navigation