alternating direction method of multipliers for nonlinear inverse problems?

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I have a standard inverse problem with L1 regularization: $\|F(\mathbf{x})-\mathbf{y}\|^2_2+\alpha\|\mathbf{x}\|_1$, where $F(\mathbf{x})$ is nonlinear. I am wondering if this is a good problem to use ADMM. Or should I just use a usual L1 solver.
Thanks in advance.