Tight error bounds for nonnegative orthogonality constraints and exact penalties
For the intersection of the Stiefel manifold and the set of nonnegative matrices in $\mathbb
{R}^{n\times r} $, we present global and local error bounds with easily computable residual …
{R}^{n\times r} $, we present global and local error bounds with easily computable residual …
Tight error bounds for the sign-constrained Stiefel manifold
X Chen, Y He, Z Zhang - SIAM Journal on Optimization, 2025 - SIAM
The sign-constrained Stiefel manifold in is a segment of the Stiefel manifold with fixed signs
(nonnegative or nonpositive) for some entries of the matrices. It includes the nonnegative …
(nonnegative or nonpositive) for some entries of the matrices. It includes the nonnegative …
非负正交约束优化问题的理论, 算法及应用
姜波 - 运筹学学报, 2023 - ort.shu.edu.cn
非负正交约束优化问题是同时带有非负约束和正交约束的优化问题, 该类问题在机器学习和数据
科学中有着重要的应用. 常见的非负正交约束优化问题包括二次指派问题, 图匹配问题 …
科学中有着重要的应用. 常见的非负正交约束优化问题包括二次指派问题, 图匹配问题 …
Error bounds for rank-one DNN reformulation of QAP and DC exact penalty approach
Y Qian, S Pan, S Bi, H Qi - arXiv preprint arXiv:2403.11210, 2024 - arxiv.org
This paper concerns the quadratic assignment problem (QAP), a class of challenging
combinatorial optimization problems. We provide an equivalent rank-one doubly …
combinatorial optimization problems. We provide an equivalent rank-one doubly …
A relaxation method for binary orthogonal optimization problems with its applications
L Xiao, Y Qian, S Pan - arXiv preprint arXiv:2308.10506, 2023 - arxiv.org
This paper focuses on a class of binary orthogonal optimization problems frequently arising
in semantic hashing. Consider that this class of problems may have an empty feasible set …
in semantic hashing. Consider that this class of problems may have an empty feasible set …
No Wrong Turns: The Simple Geometry Of Neural Networks Optimization Paths
Understanding the optimization dynamics of neural networks is necessary for closing the
gap between theory and practice. Stochastic first-order optimization algorithms are known to …
gap between theory and practice. Stochastic first-order optimization algorithms are known to …