Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Lai, Lexiao"'
Autor:
Lai, Lexiao
Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where assumptions of
Externí odkaz:
http://arxiv.org/abs/2412.00640
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 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, 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, 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
Autor:
Josz, Cédric, Lai, Lexiao
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
Externí odkaz:
http://arxiv.org/abs/2211.14848
Autor:
Josz, Cédric1 (AUTHOR) cj2638@columbia.edu, Lai, Lexiao1 (AUTHOR)
Publikováno v:
Mathematical Programming. Sep2024, Vol. 207 Issue 1/2, p551-576. 26p.
Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its target while minimizing the cumulative exposure to a moving enemy Obse
Externí odkaz:
http://arxiv.org/abs/1903.01332