3 papers
math.OC2026
A Fletcher's Augmented Lagrangian-Based Stochastic First-Order Method for Nonconvex Equality-Constrained Optimization
Yawen Cui, Qiankun Shi, Xiao Wang +1
In this paper, we study nonconvex equality-constrained optimization problems in which only stochastic first-order approximations of the objective and constraint functions are avail…
math.RA2026
The Geometric Origin of the Cayley-Hamilton Theorem: A Constructive Proof via Dimensional Syzygy
Xiao Wang
We demonstrate that the Cayley-Hamilton theorem is a derived consequence of a more fundamental dimensional constraint: the syzygy formed by the tensor product of two Levi-Civita sy…
math.OC2025
Adaptive directional decomposition methods for nonconvex constrained optimization
Qiankun Shi, Xiao Wang
In this paper, we study nonconvex constrained optimization problems with both equality and inequality constraints, covering deterministic and stochastic settings. We propose a nove…