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C1,1 functions and optimality conditions

Author

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  • Davide La Torre
  • Matteo Rocca

Abstract

In this work we provide a characterization of C1,1 functions on Rn (that is,diferentiable with locally Lipschitz partial derivatives) by means of second directional divided differences. In particular, we prove that the class of C1,1 functions is equivalent to the class of functions with bounded second directional divided diferences. From this result we deduce a Taylor's formula forthis 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.

Suggested Citation

  • Davide La Torre & Matteo Rocca, 2002. "C1,1 functions and optimality conditions," Departmental Working Papers 2002-13, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2002-13
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    File URL: http://wp.demm.unimi.it/files/wp/2002/DEMM-2002_013wp.pdf
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    References listed on IDEAS

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    1. La Torre Davide & Rocca Matteo, "undated". "A characterization of Ck,1 functions," Economics and Quantitative Methods qf0103, Department of Economics, University of Insubria.
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    Cited by:

    1. Paruolo Paolo, 2002. "Common features and common I(2) trends in VAR systems," Economics and Quantitative Methods qf0217, Department of Economics, University of Insubria.
    2. Davide La Torre & Matteo Rocca, 2003. "On C^(1,1) constrained optimation problems," Departmental Working Papers 2003-06, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Ginchev Ivan & Guerraggio Angelo & Rocca Matteo, 2003. "From scalar to vector optimization," Economics and Quantitative Methods qf0305, Department of Economics, University of Insubria.
    4. 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.
    5. 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.
    6. Davide La Torre & Carlo Vercellis, 2002. "C1,1 approximations of generalized support vector machines," Departmental Working Papers 2002-19, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    7. Davide La Torre & Matteo Rocca, 2002. "A survey on C1,1 functions: Theory, numerical methods and applications," Departmental Working Papers 2002-12, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    8. Davide LaTorre, 2002. "On generalized derivatives for C1,1 vector functions and optimality conditions," Departmental Working Papers 2002-20, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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    More about this item

    Keywords

    Divided di erences; Riemann derivatives; C1; 1 functions; nonlinear;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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