Geodesic
A characterization of $C^{1,1}$ functions via lower directional derivatives
Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 217-221

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MR Zbl
The notion of $\tilde {\ell }$-stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of $\tilde {\ell }$-stable functions coincides with the class of C$^{1,1}$ functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp.\ 383--387.
The notion of $\tilde {\ell }$-stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of $\tilde {\ell }$-stable functions coincides with the class of C$^{1,1}$ functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp.\ 383--387.
DOI : 10.21136/MB.2009.140656
Classification : 26B05, 49K10
Keywords: second-order derivative; $C^{1, 1}$ function; $\ell $-stable function; $\tilde {\ell }$-stability 
Bednařík, Dušan; Pastor, Karel. A characterization of $C^{1,1}$ functions via lower directional derivatives. Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 217-221. doi: 10.21136/MB.2009.140656
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[2] Bednařík, D., Pastor, K.: Errata: Elimination of strict convergence in optimization. SIAM J. Control Optim. 45 (2006), 383-387. | DOI | MR

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