Skip to main content
SpringerLink
Log in

Variational Analysis of Directional Minimal Time Functions and Applications to Location Problems

Set-Valued and Variational Analysis Aims and scope Submit manuscript

Cite this article

Abstract

This paper is devoted to the study of directional minimal time functions that specify the minimal time for a vector to reach an object following its given direction. We provide a careful analysis of general and generalized differentiation properties of this class of functions. The analysis allows us to study a new model of facility location that involves sets.

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

References

  1. Bertsekas, D., Nedic, A., Ozdaglar, A.: Convex Analysis and Optimization. Athena Scientific, Boston (2003)

    MATH  Google Scholar 

  2. Clarke, F.H., Ledyaev, Yu.S., Stern, R.J., Wolenski, P.R.: Nonsmooth Analysis and Control Theory. Graduate Texts in Mathematics, vol. 178. Springer, New York (1998)

    Google Scholar 

  3. Colombo, G., Wolenski, P.R.: The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space. J. Glob. Optim. 28, 269–282 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gerstewitz (Tammer), C., Iwanow, E.: Dualität für Nichtkonvexe Vektor-Ptimierungsprobleme. Wiss. Z. - Tech. Hochsch. Ilmenau 31, 61–81 (1985)

    MathSciNet  Google Scholar 

  5. Göpfert, A., Riahi, H., Tammer, C., Zalinescu, C.: Variational Methods in Partially Ordered Spaces. Springer, New York (2003)

    MATH  Google Scholar 

  6. Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, I: Basic Theory, II: Applications, Grundlehren Series (Fundamental Principles of Mathematical Sciences), vols. 330 and 331. Springer, Berlin (2006)

    Book  Google Scholar 

  7. Mordukhovich, B.S., Nam, N.M.: Subgradients of minimal time functions under minimal assumptions. J. Convex Anal. 18, 915–947 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Rockafellar, R.T., Wets, R.J.-B.: Variational Analysis. Springer, Berlin (1998)

    Book  MATH  Google Scholar 

  9. Tammer, C., Zălinescu, C.: Lipschitz properties of the scalarization function and applications. Optimization 59, 305–319 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fariborz Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR, 97202, USA

    Nguyen Mau Nam

  2. Faculty of Mathematics, University Alexandru Ioan Cuza, Iasi, Romania

    Constantin Zălinescu

  3. Octav Mayer Institute of Mathematics (Romanian Academy), Iasi, Romania

    Constantin Zălinescu

Authors
  1. Nguyen Mau Nam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Constantin Zălinescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nguyen Mau Nam.

Additional information

The research of Nguyen Mau Nam was partially supported by the Simons Foundation under grant #208785.

The research of C. Zalinescu was supported by the grant PN-II-ID-PCE-2011-3-0084, CNCS-UEFISCDI, Romania.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Nam, N.M., Zălinescu, C. Variational Analysis of Directional Minimal Time Functions and Applications to Location Problems. Set-Valued Var. Anal 21, 405–430 (2013). https://doi.org/10.1007/s11228-013-0232-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11228-013-0232-9

Keywords

Mathematics Subject Classifications (2010)

search

Navigation