12 papers
Decentralized Stochastic Subgradient-type Methods with Communication Compression for Nonsmooth Nonconvex Optimization
Siyuan Zhang, Nachuan Xiao, Xin Liu
In this paper, we consider the nonsmooth nonconvex decentralized optimization problem, where inter-agent communication is compressed. We propose a general framework that unifies va…
Exact Quadratic Penalty Function for Symplectic Eigenvalue Problem
Jiaqi Wang, Nachuan Xiao, Xin Liu
The symplectic eigenvalue problem for symmetric positive-definite (spd) matrices plays a crucial role in various scientific fields, including quantum mechanics and control theory.…
A Smooth Locally Exact Penalty Method for Optimization Problems over Generalized Stiefel Manifolds
Linshuo Jiang, Nachuan Xiao, Xin Liu
In this paper, we consider a class of optimization problems constrained to the generalized Stiefel manifold. Such problems are fundamental to a wide range of real-world application…
Convergence-Guaranteed Algorithms for l1/2-Regularized Quadratic Programs with Assignment Constraints
Lijun Xie, Ran Gu, Xin Liu
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output de…
A Tight SDP Relaxation for the Cubic-Quartic Regularization Problem
Jinling Zhou, Xin Liu, Jiawang Nie +1
This paper studies how to compute global minimizers of the cubic-quartic regularization (CQR) problem \[ \min_{s \in \mathbb{R}^n} \quad f_0+g^Ts+\frac{1}{2}s^THs+\fracβ{6}\| s \|^…
Partial Envelope for Optimization Problem with Nonconvex Constraints
Xiaoyin Hu, Xin Liu, Kim-Chuan Toh +1
In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set , where is a closed convex subset…
A Hybrid Subgradient Method for Nonsmooth Nonconvex Bilevel Optimization
Nachuan Xiao, Xiaoyin Hu, Xin Liu +1
In this paper, we focus on the nonconvex-nonconvex bilevel optimization problem (BLO), where both upper-level and lower-level objectives are nonconvex, with the upper-level problem…
Stochastic optimization over expectation-formulated generalized Stiefel manifold
Linshuo Jiang, Nachuan Xiao, Xin Liu
In this paper, we consider a class of stochastic optimization problems over the expectation-formulated generalized Stiefel manifold (SOEGS), where the objective function is con…
A Double Tracking Method for Optimization with Decentralized Generalized Orthogonality Constraints
Lei Wang, Nachuan Xiao, Xin Liu
In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distri…
Learning-rate-free Momentum SGD with Reshuffling Converges in Nonsmooth Nonconvex Optimization
Xiaoyin Hu, Nachuan Xiao, Xin Liu +1
In this paper, we propose a generalized framework for developing learning-rate-free momentum stochastic gradient descent (SGD) methods in the minimization of nonsmooth nonconvex fu…
Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions
Siyuan Zhang, Nachuan Xiao, Xin Liu
In this paper, we focus on the decentralized stochastic subgradient-based methods in minimizing nonsmooth nonconvex functions without Clarke regularity, especially in the decentral…
An Inexact Preconditioned Zeroth-order Proximal Method for Composite Optimization
Shanglin Liu, Lei Wang, Nachuan Xiao +1
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization t…