Augmented $\ell_1$ and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm
Augmented $\ell_1$ and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm
This paper studies the long-existing idea of adding a nice smooth function to "smooth" a nondifferentiable objective function in the context of sparse optimization, in particular, the minimization of $\|\mathbf{x}\|_1+\frac{1}{2\alpha}\|\mathbf{x}\|_2^2$, where $\mathbf{x}$ is a vector, as well as the minimization of $\|\mathbf{X}\|_*+\frac{1}{2\alpha}\|\mathbf{X}\|_F^2$, where $\mathbf{X}$ is a matrix and $\|\mathbf{X}\|_*$ and …