This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

C 1,1 functions and optimality conditions

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
La Torre Davide () (Department of Economics,University of Milan, Italy)
Rocca Matteo () (Department of Economics, University of Insubria, Italy)

Additional information is available for the following registered author(s):

Abstract

In this work we provide a characterization of C 1,1 functions on Rn (that is, differentiable with locally Lipschitz partial derivatives) by means of second directional divided differences. In particular, we prove that the class of C 1,1 functions is equivalent to the class of functions with bounded second directional divided differences. From this result we deduce a Taylor's formula for this class of functions and some optimality conditions. The characterizations and the optimality conditions proved by Riemann derivatives can be useful to write minimization algorithms; in fact, only the values of the function are required to compute second order conditions.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2002_15.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0208.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 14 pages
Date of creation: Apr 2002
Date of revision:
Handle: RePEc:ins:quaeco:qf0208

Contact details of provider:
Postal: Via Ravasi 2-21100 Varese
Web page: http://eco.uninsubria.it/
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (Segreteria Dipartimento).

Related research
Keywords: divided differences; Riemann derivatives; C 1; 1 functions; nonlinear optimization; generalized derivatives;

Other versions of this item:

This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. La Torre Davide & Rocca Matteo, . "A characterization of Ck,1 functions," Economics and Quantitative Methods qf0103, Department of Economics, University of Insubria.
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Davide La Torre & Carlo Vercellis, 2002. "C1,1 approximations of generalized support vector machines," Departemental Working Papers 2002-19, Department of Economics University of Milan Italy. [Downloadable!]
  2. Davide La Torre & Matteo Rocca, 2002. "A survey on C1,1 functions: Theory, numerical methods and applications," Departemental Working Papers 2002-12, Department of Economics University of Milan Italy. [Downloadable!]
    Other versions:
  3. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "First-Order Conditions for C0,1 Constrained vector optimization," Economics and Quantitative Methods qf0307, Department of Economics, University of Insubria. [Downloadable!]
  4. Davide LaTorre, 2002. "On generalized derivatives for C1,1 vector functions and optimality conditions," Departemental Working Papers 2002-20, Department of Economics University of Milan Italy. [Downloadable!]
  5. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "From scalar to vector optimization," Economics and Quantitative Methods qf0305, Department of Economics, University of Insubria. [Downloadable!]
  6. Paruolo Paolo, 2002. "Common features and common I(2) trends in VAR systems," Economics and Quantitative Methods qf0217, Department of Economics, University of Insubria. [Downloadable!]
  7. Davide La Torre & Matteo Rocca, 2003. "On C^(1,1) constrained optimation problems," Departemental Working Papers 2003-06, Department of Economics University of Milan Italy. [Downloadable!]
  8. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2002. "C 1,1 vector optimization problems and Riemann derivatives," Economics and Quantitative Methods qf0210, Department of Economics, University of Insubria. [Downloadable!]
Statistics
Access and download statistics

Did you know? Over 80% of the top 1000 economists are registered on RePEc.

This page was last updated on 2009-11-27.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.