Zobrazeno 1 - 10
of 88
pro vyhledávání: '"Josz, Cédric"'
Autor:
Josz, Cédric, Lai, Lexiao
We consider nonsmooth rank-one symmetric matrix factorization. It has no spurious second-order stationary points.
Externí odkaz:
http://arxiv.org/abs/2410.17487
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 a global minimum for almost every initial point.
Externí odkaz:
http://arxiv.org/abs/2410.09990
We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining to near a
Externí odkaz:
http://arxiv.org/abs/2408.07182
Autor:
Josz, Cedric, Li, Xiaopeng
Given a $C^{1,1}_\mathrm{loc}$ lower bounded function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ definable in an o-minimal structure on the real field, we show that the singular perturbation $\epsilon \searrow 0$ in the heavy ball system \begin{equation}
Externí odkaz:
http://arxiv.org/abs/2407.15044
Autor:
Josz, Cédric, Lai, Lexiao
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 if the method is approximated by subgradient trajectories, then the i
Externí odkaz:
http://arxiv.org/abs/2308.00899
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 us to establish local convergence, global convergence, and convergenc
Externí odkaz:
http://arxiv.org/abs/2307.03331
Autor:
Josz, Cédric, Li, Xiaopeng
Publikováno v:
SIAM Journal on Optimization, Volume 33, Issue 3, 2023
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 local minima is true in various problems of interest nowadays, includ
Externí odkaz:
http://arxiv.org/abs/2303.03536
Autor:
Josz, Cédric
Publikováno v:
Mathematical Programming 2023
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 Lipschitz gradients. We prove that global convergence holds if continuous gr
Externí odkaz:
http://arxiv.org/abs/2303.03534
Autor:
Josz, Cédric, Lai, Lexiao
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 satisfied by several spurious local minima arising in robust principal
Externí odkaz:
http://arxiv.org/abs/2211.14852
Autor:
Josz, Cédric, Lai, Lexiao
Publikováno v:
Mathematical Programming 2023
We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov stab
Externí odkaz:
http://arxiv.org/abs/2211.14850