基于卷积的绝对值函数平滑近似及其在非光滑正则化中的应用
Convolution based smooth approximations to the absolute value function with application to non-smooth regularization
AI总结：
本文提出基于卷积的绝对值函数平滑近似方法，并应用于构建非光滑正则化问题的梯度算法，以获得稀疏解。
摘要：
我们提出了新的基于卷积的绝对值函数平滑近似方法，并将其应用于构建梯度基算法，如非线性共轭梯度方案，以获得线性系统Ax = b的稀疏正则化解。与直接解决非光滑最小化问题的迭代算法不同，所提出的近似方法允许将通用非光滑稀疏诱导功能替换为可直接计算梯度和Hessians的平滑近似。所得梯度基算法通常在少数迭代中获得良好的解估计，可直接使用或快速预热现有算法。
英文摘要：
We present new convolution based smooth approximations to the absolute value function and apply them to construct gradient based algorithms such as the nonlinear conjugate gradient scheme to obtain sparse, regularized solutions of linear systems $Ax = b$, a problem often tackled via iterative algorithms which attack the corresponding non-smooth minimization problem directly. In contrast, the approximations we propose allow us to replace the generalized non-smooth sparsity inducing functional by a smooth approximation of which we can readily compute gradients and Hessians. The resulting gradient based algorithms often yield a good estimate for the sought solution in few iterations and can either be used directly or to quickly warm start existing algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
