9 papers
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…
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…
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…
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…
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…