Abstract
It is well known that, if a vector-valued function can be written as difference of componentwise convex functions, the norm of such function inherits this property. In this note we show that, if the norm in use is monotonic in the positive orthant and the functions are non-negative, a sharper decomposition can be obtained.
This is a preview of subscription content, log in via an institution to check access.
References
Blanquero R., Carrizosa E.: Optimization of the norm of a vector valued dc function and applications. J. Optim. Theory Appl. 107, 245–260 (2000)
Blanquero R., Carrizosa E.: On covering methods for dc optimization. J. Global Optim. 18, 265–274 (2000)
Blanquero R., Carrizosa E.: Continuous location problems and Big Triangle Small Triangle: constructing better bounds. J. Global Optim. 45, 389–402 (2009)
Blanquero, R., Carrizosa, E., Hansen, P.: Locating objects in the plane using global optimization techniques. Math. Oper. Res. (to appear)
Horst R., Thoai N.V.: DC programming: overview. J. Optim. Theory Appl. 103, 1–43 (1999)
Rockafellar R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
Tuy H.: DC optimization: theory, methods and algorithms. In: Horst, R., Pardalos, P.M. (eds) Handbook of Global Optimization, Kluwer, Dordrecht (1995)
Zeleny M.: Compromise programming. In: Cochrane, J.L., Zeleny, M. (eds) Multiple criteria decision making, University of South Carolina Press, Columbia (1973)
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by grants MTM2008-3032, FQM329 Spain.
Rights and permissions
About this article
Cite this article
Blanquero, R., Carrizosa, E. On the norm of a dc function. J Glob Optim 48, 209–213 (2010). https://doi.org/10.1007/s10898-009-9487-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-009-9487-y