210 citations · 451 across the 27 of their papers we have counts for
28 papers
Global stability of first-order methods for coercive tame functions
Cédric Josz, Lexiao Lai
We consider first-order methods with constant step size for minimizing locally Lipschitz coercive functions that are tame in an o-minimal structure on the real field. We prove that…
Convergence of the momentum method for semialgebraic functions with locally Lipschitz gradients
Cédric Josz, Lexiao Lai, Xiaopeng Li
We propose a new length formula that governs the iterates of the momentum method when minimizing differentiable semialgebraic functions with locally Lipschitz gradients. It enables…
Certifying the absence of spurious local minima at infinity
Cédric Josz, Xiaopeng Li
When searching for global optima of nonconvex unconstrained optimization problems, it is desirable that every local minimum be a global minimum. This property of having no spurious…
Global convergence of the gradient method for functions definable in o-minimal structures
Cédric Josz
We consider the gradient method with variable step size for minimizing functions that are definable in o-minimal structures on the real field and differentiable with locally Lipsch…
Nonsmooth rank-one matrix factorization landscape
Cédric Josz, Lexiao Lai
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 conje…
Sufficient conditions for instability of the subgradient method with constant step size
Cédric Josz, Lexiao Lai
We provide sufficient conditions for instability of the subgradient method with constant step size around a local minimum of a locally Lipschitz semi-algebraic function. They are s…