Mert Gürbüzbalaban, Michael L Overton
M Gürbüzbalaban, ML Overton Nonlinear Analysis: Theory, Methods & Applications 75 (3), 1282-1289
Publication year: 2012

We discuss two nonsmooth functions on R n introduced by Nesterov. We show that the first
variant is partly smooth in the sense of Lewis and that its only stationary point is the global
minimizer. In contrast, we show that the second variant has 2 n− 1 Clarke stationary points,
none of them local minimizers except the global minimizer, but also that its only
Mordukhovich stationary point is the global minimizer. Nonsmooth optimization algorithms
from multiple starting points generate iterates that approximate all 2 n− 1 Clarke stationary
points, not only the global minimizer, but it remains an open question as to whether the
nonminimizing Clarke stationary points are actually points of attraction for optimization
algorithms.

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