Geodesic
On weak sharp minima for a special class of nonsmooth functions
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 2, pp. 195-207.

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We present a characterization of weak sharp local minimizers of order one for a function f: ℝⁿ → ℝ defined by f(x): = maxf_i(x)| i = 1,...,p, where the functions f_i are strictly differentiable. It is given in terms of the gradients of f_i and the Mordukhovich normal cone to a given set on which f is constant. Then we apply this result to a smooth nonlinear programming problem with constraints.
Keywords: weak sharp minimizer of order one, maximum function, strictly differentiable function, normal cone 
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Studniarski, Marcin. On weak sharp minima for a special class of nonsmooth functions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 2, pp. 195-207. http://geodesic.mathdoc.fr/item/DMDICO_2000_20_2_a3/

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