C 1,1 functions and optimality conditions

Davide La Torre and Rocca Matteo ()
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Rocca Matteo: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

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.

Keywords: divided differences; Riemann derivatives; C 1; 1 functions; nonlinear optimization; generalized derivatives (search for similar items in EconPapers)
Pages: 14 pages
Date: 2002-04
New Economics Papers: this item is included in nep-cmp
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Citations: View citations in EconPapers (9)

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Related works:
Working Paper: C1,1 functions and optimality conditions (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf0208

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