## Augmented l1 and nuclear-norm models with a globally linearly convergent algorithmM. Lai and W. Yin Published in ## OverviewThe augmented Lagrange dual problem and nuclear-norm models have very interesting theoretical and numerical properties. there exists a (data-dependent) such that as long as , the solutions to the above problems are also solutions to their original problems without and , respectively; to recover sparse and low-rank , given a certain RIP condition (or NSP, SSP, RIPless condtions), one can choose and and enjoy the stable recover and , respectively; their Lagrange dual problems are unconstrained and continuously differentiable; the Lagrange dual of the augmented problem has a property that we call *restricted strongly convex*, which together with the gradient Lipschitz property enables gradient descent (and its accelerations) to converge at a linear rate , for some , in the global sense.
The paper also study their relaxed versions with and , respectively. ## CodeMatlab demos of different versions of linearized Bregman ## Citation
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