7 papers
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…
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…
Stochastic Subgradient Methods with Guaranteed Global Stability in Nonsmooth Nonconvex Optimization
Nachuan Xiao, Xiaoyin Hu, Kim-Chuan Toh
In this paper, we focus on providing convergence guarantees for stochastic subgradient methods in minimizing nonsmooth nonconvex functions. We first investigate the global stabilit…
CDOpt: A Python Package for a Class of Riemannian Optimization
Nachuan Xiao, Xiaoyin Hu, Xin Liu +1
Optimization over the embedded submanifold defined by constraints has attracted much interest over the past few decades due to its wide applications in various areas. Pl…
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…