In this paper, we characterize data-time tradeoffs of the proximal-gradient homotopy method used for solving linear inverse problems under sub-Gaussian measurements. Our results are sharp up to an absolute constant factor. We demonstrate that, in the absence of the strong convexity assumption, the proximal-gradient homotopy update can achieve a linear rate of convergence when the number of measurements is sufficiently large. Numerical simulations are provided to verify our theoretical results.

翻译：在本文中,我们描述用于解决亚高加索测量线性反问题的最接近高度的同质式方法的数据-时间取舍。我们的结果直达一个绝对不变系数。我们证明,如果没有强烈的顺流假设,在测量数量足够大的情况下,最接近高度的同质式更新可以达到线性趋同率。提供了数字模拟来验证我们的理论结果。