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On weak sharp minima for a special class of nonsmooth functions

Marcin Studniarski — 2000

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We present a characterization of weak sharp local minimizers of order one for a function f: ℝⁿ → ℝ defined by f ( x ) : = m a x f 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.

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