Before revision:  In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require to solve the lower-level problem exactly. We provide global convergence and worst-case complexity analysis of our approach, and test our proposed framework on ROF-denoising and learning MRI sampling patterns.
After revision:  In this work we propose to solve these problems using inexact derivative-free optimization algorithms which never require to solve the lower-level problem solutions, but instead assume access to approximate solutions with controllable accuracy, which is achievable in practice. We prove global convergence and worst-case complexity analysis of our approach, and test our proposed framework on ROF-denoising and learning MRI sampling patterns.