A family of second-order methods for convex \(\ell _1\) -regularized optimization

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• 作者：Richard H. Byrd ; Gillian M. Chin ; Jorge Nocedal ; Figen Oztoprak
• 刊名：Mathematical Programming
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：159
• 期：1-2
• 页码：435-467
• 全文大小：865 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Mathematics of Computing
  Numerical Analysis
  Combinatorics
  Mathematical and Computational Physics
  Mathematical Methods in Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-4646
• 卷排序：159

文摘

This paper is concerned with the minimization of an objective that is the sum of a convex function f and an \(\ell _1\) regularization term. Our interest is in active-set methods that incorporate second-order information about the function f to accelerate convergence. We describe a semismooth Newton framework that can be used to generate a variety of second-order methods, including block active set methods, orthant-based methods and a second-order iterative soft-thresholding method. The paper proposes a new active set method that performs multiple changes in the active manifold estimate at every iteration, and employs a mechanism for correcting these estimates, when needed. This corrective mechanism is also evaluated in an orthant-based method. Numerical tests comparing the performance of three active set methods are presented.Mathematics Subject Classification49M3790C3065K05