Name: Anonymous 2017-03-07 10:28
\(\begin{aligned} &partial_\varepsilon f (x) = \bigg\{x^{\ast}\in X^{\ast}:\\ &\quad\liminf_ {u \to x} \frac {f (u) -f (x) - \langle x^{\ast}, u-x \rangle} {\| u-x\|} \ge -\varepsilon \bigg\}\;,\\ &\partial_\varepsilon^+ f (x) = \bigg\{x^{\ast}\in X^{\ast}:\\ &\quad\limsup_ {u \to x} \frac {f (u) -f (x) - \langle x^{\ast}, u-x \rangle} {\| u-x\|} \le \varepsilon \bigg\}\;. \end{aligned}\)
Fréchet Subdifferentials, Encyclopedia of Optimization (2009) 7:2651-2658, January 01, 2009
Fréchet Subdifferentials, Encyclopedia of Optimization (2009) 7:2651-2658, January 01, 2009