An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization

@article{Lin2014AnAA,
  title={An Adaptive Accelerated Proximal Gradient Method and its Homotopy Continuation for Sparse Optimization},
  author={Qihang Lin and Lin Xiao},
  journal={Comp. Opt. and Appl.},
  year={2014},
  volume={60},
  pages={633-674}
}
We first propose an adaptive accelerated proximal gradient (APG) method for minimizing strongly convex composite functions with unknown convexity parameters. This method incorporates a restarting scheme to automatically estimate the strong convexity parameter and achieves a nearly optimal iteration complexity. Then we consider thel1-regularized leastsquares ( l1-LS) problem in the high-dimensional setting. Although such an objective function is not strongly convex, it has restricted strong… CONTINUE READING
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