Skip to main content
Log in

On a Zero Duality Gap Result in Extended Monotropic Programming

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

Abstract

In this note we correct and improve a zero duality gap result in extended monotropic programming given by Bertsekas (J. Optim. Theory Appl. 139:209–225, 2008).

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bertsekas, D.P.: Extended monotropic programming and duality. J. Optim. Theory Appl. 139, 209–225 (2008)

    Article  MathSciNet  Google Scholar 

  2. Rockafellar, R.T.: Monotropic programming: descent algorithms and duality. In: Mangasarian, O.L., Meyer, R.R., Robinson, S.M. (eds.) Nonlinear Programming, vol. 4, pp. 327–366. Academic Press, San Diego (1981)

    Google Scholar 

  3. Rockafellar, R.T.: Network Flows and Monotropic Optimization. Wiley, New York (1984). Republished by Athena Scientific, Belmont (1998)

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  5. Boţ, R.I., Wanka, G.: A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. Nonlinear Anal. 64, 2787–2804 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ekeland, I., Temam, R.: Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976)

    MATH  Google Scholar 

  7. Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)

    MATH  Google Scholar 

  8. Hiriart-Urruty, J.-B., Phelps, R.R.: Subdifferential calculus using ε-subdifferentials. J. Funct. Anal. 118, 54–166 (1993)

    MathSciNet  Google Scholar 

  9. Hantoute, A., López, M.A., Zălinescu, C.: Subdifferential calculus rules in convex analysis: a unifying approach via pointwise supremum functions. SIAM J. Optim. 19, 863–882 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dinh, N., López, M.A., Volle, M.: Functional inequalities in the absence of convexity and lower semicontinuity with applications to optimization. Preprint available at http://www.eio.ua.es/busqueda/publicacion.asp?p=1&c=10 (2009)

  11. López, M.A., Volle, M.: On the subdifferential of the supremum of an arbitrary family of extended real-valued functions. Preprint available at http://www.eio.ua.es/busqueda/publicacion.asp?sp=1&c=10 (2009)

  12. Fang, D.H., Li, C., Ng, K.F.: Constraint qualifications for extended Farkas’s lemmas and Lagrangian dualities in convex infinite programming. SIAM J. Optim. 20, 1311–1332 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Li, C., Fang, D., López, G., López, M.A.: Stable and total Fenchel duality for convex optimization problems in locally convex spaces. SIAM J. Optim. 20, 1032–1051 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. I. Boţ.

Additional information

Communicated by J.-C. Yao.

The authors are grateful to an anonymous reviewer for his/her remarks.

Research of R.I. Boţ was partially supported by DFG (German Research Foundation), project WA 922/1-3.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boţ, R.I., Csetnek, E.R. On a Zero Duality Gap Result in Extended Monotropic Programming. J Optim Theory Appl 147, 473–482 (2010). https://doi.org/10.1007/s10957-010-9733-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-010-9733-y

Keywords

Navigation