论文标题
牛顿型方法具有近端梯度步骤，用于稀疏估计
Newton-type Methods with the Proximal Gradient Step for Sparse Estimation
论文作者
论文摘要
在本文中，我们提出了新的方法，以有效地解决稀疏估计中遇到的凸优化问题，其中包括一种新的准牛顿方法，避免了计算Hessian矩阵并提高效率，我们证明了其快速收敛。我们还证明了牛顿方法在较弱的假设下的局部收敛性。我们提出的方法提供了一种更有效和有效的方法，尤其是对于L1正则化和组正规化问题，因为它们涉及每次更新的可变选择。通过数值实验，我们证明了方法在稀疏估计中遇到的问题中的效率。我们的贡献包括有关各种问题的理论保证和实际应用。
In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove its fast convergence. We also prove the local convergence of the Newton method under weaker assumptions. Our proposed methods offer a more efficient and effective approach, particularly for L1 regularization and group regularization problems, as they involve variable selection with each update. Through numerical experiments, we demonstrate the efficiency of our methods in solving problems encountered in sparse estimation. Our contributions include theoretical guarantees and practical applications for various problems.
