• Mathematics, Computer Science
  • Published in SIAM Journal on Optimization 2008
  • DOI:10.1137/070698920

Fixed-Point Continuation for l1-Minimization: Methodology and Convergence

@article{Hale2008FixedPointCF,
  title={Fixed-Point Continuation for l1-Minimization: Methodology and Convergence},
  author={Elaine T. Hale and Wotao Yin and Yin Zhang},
  journal={SIAM Journal on Optimization},
  year={2008},
  volume={19},
  pages={1107-1130}
}
We present a framework for solving the large-scale $\ell_1$-regularized convex minimization problem:\[ \min\|x\|_1+\mu f(x). \] Our approach is based on two powerful algorithmic ideas: operator-splitting and continuation. Operator-splitting results in a fixed-point algorithm for any given scalar $\mu$; continuation refers to approximately following the path traced by the optimal value of $x$ as $\mu$ increases. In this paper, we study the structure of optimal solution sets, prove finite… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 66 REFERENCES

Signal Recovery by Proximal Forward-Backward Splitting

  • Multiscale Modeling & Simulation
  • 2005
VIEW 8 EXCERPTS
HIGHLY INFLUENTIAL

A numerical study on fixed point continuation method applied to compressed sensing

E. Hale, W. Yin, Y. Zhang
  • Rice University CAAM Technical report TR08-24, Rice University, Houston, TX
  • 2008
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Convex Analysis

  • Princeton Landmarks in Mathematics and Physics
  • 1970
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL