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arXiv · 2208.12183

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

Mengqi Hu·Yifei Lou·Bao Wang·Ming Yan·Xiu Yang·Qiang Ye
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Abstract

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.

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Mengqi Hu, Yifei Lou, Bao Wang, Ming Yan, Xiu Yang, Qiang Ye. 2022-08-25. Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum. https://doi.org/10.1007/s10915-023-02148-y

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