论文标题
通过非线性结合梯度动量通过梯度下降加速稀疏恢复
Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum
论文作者
论文摘要
本文应用了非线性偶联梯度的自适应动量的想法，以加速稀疏恢复中的优化问题。具体而言，我们考虑了两种最小化问题：A（单）可区分函数和非平滑函数和可区分函数的总和。在第一种情况下，我们采用固定的步长以避免传统的线路搜索并建立针对二次问题的拟议算法的收敛分析。这种加速度进一步与操作员分裂技术一起纳入，以处理第二种情况下的非平滑函数。我们使用凸$ \ ell_1 $和非convex $ \ ell_1- \ ell_2 $函数用作两个案例研究，以证明所提出的方法比传统方法的效率。
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. We use the convex $\ell_1$ and the nonconvex $\ell_1-\ell_2$ functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.
