Year: 2026
Type: preprint
Abstract: Composite optimization plays a central role in modern machine learning and signal processing, as it offers a natural balance between data fidelity and structural properties. In this paper, we study composite optimization in the setting where both components are nonsmooth and nonconvex. We start with a deterministic Bregman proximal subgradient method that converges under subgradient upper-bound conditions. This approach relaxes the standard requirement on the convexity of the regularization term, thus accommodating a broader range of applications. To extend this to the stochastic regime, we develop a model-based minimization method under a relative Lipschitz condition and establish a convergence rate of $\mathcal{O}(\varepsilon^{-4})$. We also extend the framework with convergence guarantees to the setting where the distance generating function and its gradient are accessible only through a stochastic oracle.
Source: arXiv (Cornell University)
Authors: Jiang, Chen, Bi, Jiawen, Zhang, Shuzhong
Institutions: University of Minnesota, University of Minnesota System
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204790827
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