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• W2019465316 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 calculate. We show that the worst-case complexity of reaching an $epsilon$ scaled stationary point is $O(epsilon^{-2})$. Moreover, if the objective function is locally Lipschitz continuous, the SQR algorithm with a slightly modified updating scheme for the smoothing parameter and iterate can obtain an $epsilon$ Clarke stationary point in at most $O(epsilon^{-3})$ iterations." @default.
• W2019465316 created "2016-06-24" @default.
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• W2019465316 date "2013-01-01" @default.
• W2019465316 modified "2023-10-16" @default.
• W2019465316 title "Worst-Case Complexity of Smoothing Quadratic Regularization Methods for Non-Lipschitzian Optimization" @default.
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• W2019465316 doi "https://doi.org/10.1137/120864908" @default.
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