Nachuan Xiao

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…

A Single-Loop Regularized Newton Method for Nonconvex-Strongly-Concave Minimax Optimization

Bohao Ma, Nachuan Xiao, Junyu Zhang

For smooth nonconvex-strongly-concave minimax problems, existing second-order methods share a common double-loop structure where the inner maximization is solved to sufficiently hi…

Improved Penalty Function Approaches for Optimization Problems with General Orthogonality

Yongshen Zhang, Xin Liu, Nachuan Xiao +1

In this paper, we consider a class of generalized orthogonal optimization constraint problems (GOOCP) over $R^{n \times p}$ , where the variable $X$ is restricted within th…

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…

Line-search and Adaptive Step Sizes for Nonconvex-strongly-concave Minimax Optimization

Bohao Ma, Nachuan Xiao, Junyu Zhang

In this paper, we propose a novel reformulation of the smooth nonconvex-strongly-concave (NC-SC) minimax problems that casts the problem as a joint minimization. We show that our r…

A Quadratically Convergent Alternating Projection Method for Nonconvex Sets

Nachuan Xiao, Shiwei Wang, Tianyun Tang +1

In this paper, we consider the feasibility problem, which aims to find a feasible point for the constraint set ${x \in R^{n} : c (x) = 0}$ over a possibly non-regular subset…

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 ${x \in X : c (x) = 0}$ , where $X$ is a closed convex subset…

An Exact Penalty Approach for Equality Constrained Optimization over a Convex Set

Nachuan Xiao, Tianyun Tang, Shiwei Wang +1

In this paper, we consider the nonlinear constrained optimization problem (NCP) with constraint set ${x \in X : c (x) = 0}$ , where $X$ 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 $f$ 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…

A Minimization Approach for Minimax Optimization with Coupled Constraints

Xiaoyin Hu, Kim-Chuan Toh, Shiwei Wang +1

In this paper, we focus on the nonconvex-strongly-concave minimax optimization problem (MCC), where the inner maximization subproblem contains constraints that couple the primal va…

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…

Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization

Nachuan Xiao, Kuangyu Ding, Xiaoyin Hu +1

In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f (x)$ over a closed convex subset $X$ of $R^{n}$ , with additional nonsmoot…

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…