Worst-Case Complexity of Smoothing Quadratic Regularization Methods for Non-Lipschitzian Optimization

@article{Bian2013WorstCaseCO,
  title={Worst-Case Complexity of Smoothing Quadratic Regularization Methods for Non-Lipschitzian Optimization},
  author={Wei Bian and Xiaojun Chen},
  journal={SIAM Journal on Optimization},
  year={2013},
  volume={23},
  pages={1718-1741}
}
Abstract. In this paper, we propose a smoothing quadratic regularization (SQR) algorithm for solving a class of nonsmooth nonconvex, perhaps even non-Lipschitzian minimization problems, which has wide applications in statistics and sparse reconstruction. The proposed SQR algorithm is a first order method. At each iteration, the SQR algorithm solves a strongly convex quadratic minimization problem with a diagonal Hessian matrix, which has a simple closed-form solution that is inexpensive to… CONTINUE READING