Skip to main content
SpringerLink
Log in

A Note on the Existence of Nonsmooth Nonconvex Optimization Problems

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Sufficient conditions for the existence of a solution to an abstract optimization problem in Banach spaces are given, which do not rely on convexity, regularity properties or a straightforward coerciveness assumption. Applications to sparsity-constrained optimization and to problems from mechanics are provided.

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. Baiocchi, C., Buttazzo, G., Gastaldi, F., Tomarelli, F.: General existence theorems for unilateral problems in continuum mechanics. Arch. Ration. Mech. Anal. 100, 149–189 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  2. Auslender, A., Teboulle, M.: Asymptotic Cones and Functions in Optimization and Variational Inequalities. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  3. Penot, J.-P.: Noncoercive problems and asymptotic conditions. Asymptot. Anal. 49, 205–215 (2006)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

K. Ito research partially supported by US-ARO grant 49308-MA and US-AFSOR grant FA 9550-06-1-0241. K. Kunisch supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung under SFB 32, “Mathematical Optimization and Applications in the Biomedical Sciences”.

Author information

Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC , 27695-8205, USA

    Kazufumi Ito

  2. Institut für Mathematik, Karl-Franzens-Universität Graz, 8010 , Graz, Austria

    Karl Kunisch

Authors
  1. Kazufumi Ito
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karl Kunisch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karl Kunisch.

Additional information

Communicated by Giuseppe Buttazzo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ito, K., Kunisch, K. A Note on the Existence of Nonsmooth Nonconvex Optimization Problems. J Optim Theory Appl 163, 697–706 (2014). https://doi.org/10.1007/s10957-014-0552-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-014-0552-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation