15 citations · 17 across the 14 of their papers we have counts for
14 papers
An Infeasible Method with Feasibility Safeguard for Nonsmooth Composite Optimization Over Manifolds
Xiyua Xie, Qia Li
We study nonsmooth composite optimization over embedded submanifolds defined by nonlinear equality constraints. We propose a feasibility-safeguarded inexact proximal linearized met…
Local Convergence Analysis of ADMM for Nonconvex Composite Optimization
Xiyuan Xie, Lihua Yang, Qia li
In this paper, we study the local convergence of the standard ADMM scheme for a class of nonconvex composite optimization problems motivated by applications in signal processing an…
An efficient proximal algorithm for squared L1 over L2 regularized sparse recovery
Na Zhang, Hong Chen, Qia Li +1
In this paper, we consider a squared regularized model for sparse signal recovery from noisy measurements. We first establish the existence of optimal solutions to the mo…
Proximal Gradient Descent Ascent Methods for Nonsmooth Nonconvex-Concave Minimax Problems on Riemannian Manifolds
Xiyuan Xie, Qia Li
Nonsmooth nonconvex-concave minimax problems have attracted significant attention due to their wide applications in many fields. In this paper, we consider a class of nonsmooth non…
A min-max reformulation and proximal algorithms for a class of structured nonsmooth fractional optimization problems
Junpeng Zhou, Na Zhang, Qia Li
In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function…
Proximal methods for structured nonsmooth optimization over Riemannian submanifolds
Qia Li, Na Zhang, Junyu Feng +1
In this paper, we consider a class of structured nonsmooth optimization problems over an embedded submanifold of a Euclidean space, where the first part of the objective is the sum…
An equivalent reformulation and multi-proximity gradient algorithms for a class of nonsmooth fractional programming
Junpeng Zhou, Na Zhang, Qia Li
In this paper, we consider a class of structured fractional programs, where the numerator part is the sum of a block-separable (possibly nonsmooth nonconvex) function and a locally…
A Successive Two-stage Method for Sparse Generalized Eigenvalue Problems
Qia Li, Jianmin Liao, Lixin Shen +1
The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant…
Parameterized proximal-gradient algorithms for L1/L2 sparse signal recovery
Na Zhang, Xinrui Liu, Qia Li
The ratio of L1 and L2 norms (L1/L2), serving as a sparse promoting function, receives considerable attentions recently due to its effectiveness for sparse signal recovery. In this…
Smoothing algorithms for nonsmooth and nonconvex minimization over the stiefel manifold
Jinlai Zhu, Jianfeng Huang, Lihua Yang +1
We consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a no…
First-order algorithms for a class of fractional optimization problems
Na Zhang, Qia Li
We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a…
Capped Lp approximations for the composite L0 regularization problem
Qia Li, Na Zhang
The composite L0 function serves as a sparse regularizer in many applications. The algorithmic difficulty caused by the composite L0 regularization (the L0 norm composed with a lin…
On optimal solutions of the constrained regularization and its penalty problem
Na Zhang, Qia Li
The constrained regularization plays an important role in sparse reconstruction. A widely used approach for solving this problem is the penalty method, of which the least…
Two-step Fixed-point proximity algorithms for multi-block separable convex problems
Qia Li, Yuesheng Xu, Na Zhang
Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear cons…