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math.OC2024
Global convergence of gradient descent for phase retrieval
Théodore Fougereux, Cédric Josz, Xiaopeng Li
We propose a tensor-based criterion for benign landscape in phase retrieval and establish boundedness of gradient trajectories. This implies that gradient descent will converge to…
math.OC2024
Nonsmooth rank-one symmetric matrix factorization landscape
Cédric Josz, Lexiao Lai
We consider nonsmooth rank-one symmetric matrix factorization. It has no spurious second-order stationary points.
math.OC2024
Proximal random reshuffling under local Lipschitz continuity
Cédric Josz, Lexiao Lai, Xiaopeng Li
We study proximal random reshuffling (PRR) for minimizing the sum of locally Lipschitz or locally smooth functions and a proper lower semicontinuous convex function without assumin…
math.DS2024
Singular perturbation in heavy ball dynamics
Cedric Josz, Xiaopeng Li
Given a lower bounded function definable in an o-minimal structure on the real field, we show that the singular pertur…