IPI
Nomonotone spectral gradient method for sparse recovery
Wanyou Cheng Zixin Chen Donghui Li
In the paper, we present an algorithm framework for the more general problem of minimizing the sum $f(x)+\psi(x)$, where $f$ is smooth and $\psi$ is convex, but possible nonsmooth. At each step, the search direction of the algorithm is obtained by solving an optimization problem involving a quadratic term with diagonal Hessian and Barzilai-Borwein steplength plus $ \psi(x)$. The nonmonotone strategy is combined with -Borwein steplength to accelerate the convergence process. The method with the nomonotone line search techniques is showed to be globally convergent. In particular, if $f$ is convex, we show that the method shares a sublinear global rate of convergence. Moreover, if $f$ is strongly convex, we prove that the method converges R-linearly. Numerical experiments with compressive sense problems show that our approach is competitive with several known methods for some standard $l_2-l_1$ problems.
keywords: Iterative shrinkage thresholding algorithm Barzilai-Borwein method. $l_1-$ regularization nonsmooth optimization

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