arXiv Machine Learning
The paper introduces the Controlled Block Proximal Linearized (CBPL) method for multiblock nonconvex and nonsmooth optimization, avoiding assumptions of bounded iterates or objective coercivity. CBPL adds a control potential to block updates while preserving the original objective, variables, and constraints, and under explicit control design conditions and the KL property it guarantees boundedness, finite length, whole‑sequence convergence of variables, and convergence of objective values. The method is applied to graph‑regularized nonnegative matrix factorization, CP decomposition, and independent‑core matrix tri‑factorization with β0 sparsity constraints, demonstrating reconstruction‑preserving scale degeneracies, explicit controls yielding compact sublevel sets, and whole‑sequence convergence to full critical points, with experiments confirming convergence and sustained graph action.
The paper introduces the Generalized Geometry Block Proximal Linearized (GGBPL) method, which uses a generalized geometry proximal linearized operator to update block variables in multiblock nonconvex and nonsmooth optimization problems. By allowing arbitrary inner products and admissible metrics, GGBPL adapts to the geometric structure of various problems, improving numerical efficiency over traditional Euclidean‑based methods. An inertial variant (iGGBPL) is also presented, and a unified convergence framework is established, proving objective convergence, global convergence to a critical point, and an ε‑stationary point iteration complexity of φ(ε−−). The methods are applied to sparse nonnegative matrix factorization and sparse nonnegative CP decomposition with λ₀ constraints, showing superior performance in numerical experiments.
By Weifeng Yang
arXiv:2608.28799v1 Announce Type: cross
Abstract: Separable nonnegative matrix factorization (SNMF) has been widely used for low-rank representation and clustering of nonnegative data, owing to its a...
By Matthew McCarver, Jing Qin
arXiv:2606. 28307v1 Announce Type: cross Abstract: We analyze Bregman ADMM for nonconvex linearly constrained problems under two-sided relative smoothness, a condition that replaces the standard Lipschitz gradient assumption with a Hessian comparison relative to a Bregman kernel.
By Shuang Li, Zhihui Zhu, Qiuwei Li
arXiv:2608. 05502v1 Announce Type: cross Abstract: In this paper, we consider a class of multiblock nonconvex nonsmooth optimization problems, which covers many applications such as the analysis of pre-earthquake anomalies and machine learning.
By Weifeng Yang
arXiv:2607. 27507v1 Announce Type: new Abstract: Matrix factorisation is a fundamental tool for exploiting low-dimensional structure in high-dimensional data, with applications such as data compression, denoising, structure discovery, interpretable representation learning, and dimensionality reduction.
By Tingting Mu
The paper introduces a deterministic Simulated Oracle Direction (SOD) framework that enables escaping spurious local minima in non‑convex low‑rank matrix sensing without explicit tensor lifting. By projecting over‑parameterized escape directions back into the original parameter space, the method guarantees a strict decrease in objective value from existing local minima. Experiments show reliable escape from local minima and convergence to global optima with minimal computational overhead compared to explicit over‑parameterization.
By Tianqi Shen, Jinji Yang, Junze He, Kunhan Gao, Zeyu Zheng, Ziye Ma
arXiv:2606. 31390v1 Announce Type: cross Abstract: Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization.
By Yudong Wei, Liang Zhang, Bingcong Li, Niao He
The paper introduces AutoConvexRelax, a learning-based framework that automates the design of convex relaxations for nonconvex optimization problems. By representing a problem as a tripartite graph of variables, symbolic terms, and objective/constraint positions, the method learns a policy to compose symbolic rewrites that generate valid relaxation trajectories. Experiments on quadratic and fractional problems show that the learned policy improves McCormick lower bounds by 13.52% and achieves near‑semidefinite bounds while using smaller formulations.
By Jinrun Liu, Bai Yan, Tengfei Liu, Qunfeng Liu, Jian Yang, Shi Cheng, Yuhui Shi, Qi Zhao
arXiv:2607. 28456v1 Announce Type: cross Abstract: Solving large, sparse linear systems is a core task in scientific computing, and efficient iterative solvers rely critically on effective and robust preconditioning.
By Zechen Zhang, Rui Peng Li, Yousef Saad
arXiv:2509.02894v2 Announce Type: replace-cross
Abstract: We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method featur...
By Adeyemi D. Adeoye, Puya Latafat, Alberto Bemporad
arXiv:2606. 08291v1 Announce Type: new Abstract: We study the symmetric multi-type orthogonal non-negative matrix tri-factorization problem, where several symmetric non-negative matrices are simultaneously approximated by factors of the form $GS_{i}G^{\top}$, with a shared non-negative and orthogonal factor $G$.
By Rok Hribar, Gregor Papa, Janez Povh, Andrej Kastrin
arXiv:2609.14307v1 Announce Type: new
Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...
By Binghao Wang, Feng Zhang, Wendong Wang, Jianjun Wang