6 citations · 6 across the 15 of their papers we have counts for
17 papers
Nonsmooth Optimization via Orthogonalized Momentum
Lexiao Lai, Tianyi Lin, Jiayu Zhang
Modern real application problems involve matrix-valued parameters, yet conventional optimizers treat them as vectors, thereby motivating matrix-aware methods that exploit input-out…
Convergence of difference inclusions: a diameter criterion and step-size conditions
Lexiao Lai, Mingzhi Song
We study bounded realizations of discrete difference inclusions with set-valued increments and additive errors. Our results have two parts. First, we give a general convergence cri…
Certifying optimality in nonconvex robust PCA
Pinxi Gong, Lexiao Lai, Jianhao Ma
Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimi…
Global convergence of the subgradient method for robust signal recovery
Zesheng Cai, Lexiao Lai, Tiansheng Li
We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives ar…
Manifold constrained steepest descent for smooth and closed-set optimization
Kaiwei Yang, Lexiao Lai
We study minimization of smooth functions over feasible sets that have smooth embedded-manifold structure throughout or only on selected regions, using linear minimization oracles…
Non-Convex Self-Concordant Functions: Practical Algorithms and Complexity Analysis
Donald Goldfarb, Lexiao Lai, Tianyi Lin +1
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two…
On the diameter of subgradient sequences in o-minimal structures
Lexiao Lai, Mingzhi Song
We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is rela…
Phase Transitions in Phase-Only Compressed Sensing
Junren Chen, Lexiao Lai, Arian Maleki
The goal of phase-only compressed sensing is to recover a structured signal from the phases under some complex-valued sen…
Stability of first-order methods in tame optimization
Lexiao Lai
Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are…
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.
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…
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…
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…
Lyapunov stability of the subgradient method with constant step size
Cédric Josz, Lexiao Lai
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 vicini…
Time-Dependent Surveillance-Evasion Games
Elliot Cartee, Lexiao Lai, Qianli Song +1
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…