5 papers
Primal-Dual Halpern-PAGE Algorithm for Constrained Stochastic Weakly Convex Optimization
Lixin Tang, Xingyu Wang, Liwei Zhang
We tackle the challenging problem of stochastic weakly convex optimization subject to mixed (equality and inequality) expected-value constraints. While optimal $\mathcal{O}(ε^{-3})…
Stability of Lagrangian Generalized Nash Equilibriums
Lixin Tang, Liwei Zhang
Lagrangian generalized Nash equilibriums (LGNEs) were introduced by Rockafellar (2024) for a class of generalized Nash equilibrium problems (GNEPs) in which each player's strategy…
Prox-PEP: A Proximal Partial Exact Penalty Algorithm for Weakly Convex Stochastic Nonlinear Programming
Lixin Tang, Xingyu Wang, Liwei Zhang
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subprobl…
Halpern Acceleration of the Inexact Proximal Point Method of Rockafellar
Liwei Zhang, Fanli Zhuang, Ning Zhang
This paper investigates a Halpern acceleration of the inexact proximal point method for solving maximal monotone inclusion problems in Hilbert spaces. The proposed Halpern inexact…
An Efficient Smoothing Damped Newton Method for Large-Scale Mathematical Programs with Equilibrium Constraints
Yixin Wang, Qingna Li, Liwei Zhang
Bilevel hyperparameter optimization has received growing attention thanks to the fast development of machine learning. Due to the tremendous size of data sets, the scale of bilevel…