We propose Dual-Feedback Generalized Proximal Gradient Descent (DFGPGD) as a new, hardware-friendly, operator splitting algorithm. We then establish convergence guarantees under approximate computational errors and we derive theoretical criteria for the numerical stability of DFGPGD based on absolute stability of dynamical systems. We also propose a new generalized proximal ADMM that can be used to instantiate most of existing proximal-based composite optimization solvers. We implement DFGPGD and ADMM on FPGA ZCU106 board and compare them in light of FPGA's timing as well as resource utilization and power efficiency. We also perform a full-stack, application-to-hardware, comparison between approximate versions of DFGPGD and ADMM based on dynamic power/error rate trade-off, which is a new hardware-application combined metric.

翻译：我们提出了一种新型硬件友好的算子分裂算法——双反馈广义近端梯度下降（DFGPGD）。随后，我们建立了在近似计算误差下的收敛性保证，并基于动力系统的绝对稳定性推导了DFGPGD数值稳定性的理论判据。我们还提出了一种新的广义近端交替方向乘子法（ADMM），可用于实例化大多数现有的基于近端法的复合优化求解器。我们在FPGA ZCU106开发板上实现了DFGPGD和ADMM，并从FPGA时序、资源利用率和能效三方面进行了对比。此外，我们还基于动态功耗/错误率权衡这一新的硬件-应用联合指标，对DFGPGD和ADMM的近似版本进行了从应用到硬件的全栈式比较。