Penalty Methods for a Class of Non-Lipschitz Optimization Problems

@article{Chen2016PenaltyMF,
  title={Penalty Methods for a Class of Non-Lipschitz Optimization Problems},
  author={Xiaojun Chen and Zhaosong Lu and Ting Kei Pong},
  journal={SIAM Journal on Optimization},
  year={2016},
  volume={26},
  pages={1465-1492}
}
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing sparsity in the solutions while the constraint set models the noise tolerance and incorporates other prior information for data fitting. To solve this class of constrained optimization… CONTINUE READING
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