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Award ID contains: 2023032

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  1. ; (, SIAM Journal on Optimization)
    We provide sufficient conditions for instability of the subgradient method with constant step size around a local minimum of a locally Lipschitz semialgebraic function. They are satisfied by several spurious local minima arising in robust principal component analysis and neural networks. 
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  2. ; (, SIAM Journal on Optimization)
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  3. ; (, Mathematical Programming)
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  4. (, Mathematical Programming)
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  5. ; (, Optimization letters)
    We provide the first positive result on the nonsmooth optimization landscape of robust principal component analysis, to the best of our knowledge. It is the object of several conjectures and remains mostly uncharted territory. We identify a necessary and sufficient condition for the absence of spurious local minima in the rank-one case. Our proof exploits the subdifferential regularity of the objective function in order to eliminate the existence quantifier from the first-order optimality condition known as Fermat’s rule. 
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