Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum
Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum
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DOI：
10.1007/s10915-023-02148-y
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发表时间：
2022-08
影响因子：
2.5
通讯作者：
Mengqi Hu;Y. Lou;Bao Wang;Ming Yan;Xiu Yang;Q. Ye
中科院分区：
文献类型：
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作者：
Mengqi Hu;Y. Lou;Bao Wang;Ming Yan;Xiu Yang;Q. Ye
本文应用非线性共轭梯度的自适应动量思想来加速稀疏恢复中的优化问题。具体来说，我们考虑了两种类型的最小化问题：一个（单一）可微函数和一个非光滑函数和一个可微函数的和。在第一种情况下，我们采用固定步长来避免传统的直线搜索，并建立了该算法对二次型问题的收敛性分析。这种加速进一步与算子分裂技术相结合，以处理第二种情况下的非光滑函数。我们用凸泛函和非凸泛函作为两个案例来证明所提出的方法相对于传统方法的有效性。
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 convexand the nonconvexfunctionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.