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math.OC2025
On Convergence of Regularized Barzilai-Borwein Method
Xin Xu
The regularized Barzilai-Borwein (RBB) method represents a promising gradient-based optimization algorithm. In this paper, by splitting the gradient into two parts and analyzing th…
math.OC2025
On Convergence and Stability of Two Extended BB-like Step Sizes
Xin Xu
The Barzilai-Borwein (BB) step sizes have a profound impact on gradient descent methods. In this work, we propose two new gradient step sizes: one longer than the original long BB…
math.OC2025
An adaptive ADMM with regularized spectral penalty for sparse portfolio selection
Xin Xu
The mean-variance (MV) model is the core of modern portfolio theory. Nevertheless, it suffers from the over-fitting problem due to the estimation errors of model parameters. We con…