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  1. No Access

    Article

    Convergence rates of training deep neural networks via alternating minimization methods

    Training deep neural networks (DNNs) is an important and challenging optimization problem in machine learning due to its non-convexity and non-separable structure. The alternating minimization (AM) approaches ...

    **tao Xu, Chenglong Bao, Wenxun **ng in Optimization Letters (2024)

  2. No Access

    Article

    A semismooth Newton based augmented Lagrangian method for nonsmooth optimization on matrix manifolds

    This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant po...

    Yuhao Zhou, Chenglong Bao, Chao Ding, Jun Zhu in Mathematical Programming (2023)

  3. No Access

    Article

    Duality for \(\alpha \) -Möbius invariant Besov spaces

    For \(1\le p\le \infty \) 1 ≤ p ...

    Guanlong Bao, Zengjian Lou, **ao**g Zhou in Banach Journal of Mathematical Analysis (2023)

  4. No Access

    Article

    Carleson measures and the range of a Cesàro-like operator acting on \(H^\infty \)

    In this paper, we determine the range of a Cesàro-like operator acting on \(H^\infty \) ...

    Guanlong Bao, Fangmei Sun, Hasi Wulan in Analysis and Mathematical Physics (2022)

  5. No Access

    Article

    \({{\cal Q}_K}\) Spaces: A Brief and Selective Survey

    This article traces several prominent trends in the development of Mobius invariant function spaces \({{\cal Q}_K}\) ...

    Guanlong Bao 鲍官龙, Hasi Wulan 乌兰哈斯 in Acta Mathematica Scientia (2021)

  6. No Access

    Article

    Closure in the Logarithmic Bloch Norm of Dirichlet Type Spaces

    In this paper, for every \(\alpha \in \mathbb {R}\) α ∈ ...

    Guanlong Bao, Zengjian Lou, **ao**g Zhou in Complex Analysis and Operator Theory (2021)

  7. No Access

    Article

    Hankel Measures for Hardy Spaces

    In this paper, we study the so-called Hankel measures on the open unit disk. We obtain several new characterizations for such measures and answer a question raised by J. **ao in 2000.

    Guanlong Bao, Fangqin Ye, Kehe Zhu in The Journal of Geometric Analysis (2021)

  8. No Access

    Article

    On the Closures of Dirichlet Type Spaces in the Bloch Space

    In this paper, via high order derivatives and via embedding derivatives of Bloch type functions into Lebesgue spaces, we characterize the closures of Dirichlet type spaces in the Bloch space. We obtain the inc...

    Guanlong Bao, Nihat Gökhan Göğüş in Complex Analysis and Operator Theory (2019)

  9. No Access

    Article

    On Multipliers of Dirichlet Type Spaces

    Let \(M(\mathcal {D}_K)\) M ...

    Guanlong Bao, Zengjian Lou, Ruishen Qian… in Complex Analysis and Operator Theory (2015)

  10. No Access

    Article

    Improving multipliers and zero sets in \(\mathcal {Q}_K\) spaces

    Let \(X\) X and...

    Guanlong Bao, Zengjian Lou, Ruishen Qian, Hasi Wulan in Collectanea Mathematica (2015)