Autori
Rocca, Matteo
La Torre, Davide

Titolo
C1,1 functions and optimality conditions
Periodico
Università degli Studi dell'Insubria. Dipartimento di Economia. Quaderni di ricerca
Anno: 2002 - Fascicolo: 15 - Pagina iniziale: 1 - Pagina finale: 12

In this work we provide a characterization of C1,1 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 C1,1 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.



Testo completo: http://eco.uninsubria.it/dipeco/quaderni/files/QF2002_15.pdf

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