5 papers · 1 filter
A Unified Framework for Iterate Convergence of Bregman Proximal Methods
He Chen, Jiaming Fan, Anthony Man-Cho So
Iterate convergence of Bregman proximal methods (BPMs) has long remained open, especially for nonconvex objectives. Recently, \citet{chen2026skl} made progress by establishing iter…
On the Iterate Convergence of Bregman Projected Gradient Method
He Chen, Anthony Man-Cho So
The iterate convergence of \textit{Bregman projected gradient method} (BPGM) has remained a long-standing open problem, especially for the widely adopted Shannon entropy kernel. Ex…
Accelerated Price Adjustment for Fisher Markets with Exact Recovery of Competitive Equilibrium
He Chen, Chonghe Jiang, Anthony Man-Cho So
The canonical price-adjustment process, tâtonnement, typically fails to converge to the exact competitive equilibrium (CE) and requires a high iteration complexity of $\tilde{\math…
Set Smoothness Unlocks Clarke Hyper-stationarity in Bilevel Optimization
He Chen, Jiajin Li, Anthony Man-Cho So
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point -- a stationary point of the hy…
Computing Competitive Equilibrium for Chores: Linear Convergence and Lightweight Iteration
He Chen, Chonghe Jiang, Anthony Man-Cho So
Competitive equilibrium (CE) for chores has recently attracted significant attention, with many algorithms proposed to approximately compute it. However, existing algorithms either…