5 papers · 1 filter
Benign Degeneracy for First-Order Methods in Exact Boolean Moment-SOS Relaxations
Shucheng Kang
Pseudo-Boolean optimization -- minimizing a polynomial over -- includes MAX-CUT, binary quadratic optimization, and Ising models. The moment-sum-of-squares (Moment-SO…
Spectral Deflation for Factorization-Free Matrix Filtering in Muon and Semidefinite Programming
Haoran Sun, Shucheng Kang, Heng Yang
GPU implementations of the Muon optimizer and of first-order semidefinite programming (SDP) solvers share one computational pattern: a matrix factorization is replaced by a fixed-d…
Afterimage Slow Regions in First-Order Methods for Linear Conic Programming
Shucheng Kang, Heng Yang
First-order methods for linear conic programming often stall on long plateaus. Existing analyses characterize when during a run or on which problem instances slow convergence occur…
Simplicial Regularizability of the Pseudo-Moment Cone and Carathéodory-Type Atomic Decomposition of Moment Matrices
Shucheng Kang, Heng Yang
We study the facial geometry of the homogeneous pseudo-moment cone \(Σ_{n,2d}^*\) and its implications for atomic decomposition of moment matrices. For fixed \(d \ge 2\), we show t…
Local Second-Order Limit Dynamics of the Alternating Direction Method of Multipliers for Semidefinite Programming
Shucheng Kang, Heng Yang
The alternating direction method of multipliers (ADMM) is widely used for solving large-scale semidefinite programs (SDPs), yet on instances with multiple primal-dual optimal solut…