A family of second-order methods for convex -regularized optimization

作者：Byrd Richard H; Chin Gillian M^*; Nocedal Jorge; Oztoprak Figen

来源：Mathematical Programming, 2016, 159(1-2): 435-467.

DOI：10.1007/s10107-015-0965-3

This paper is concerned with the minimization of an objective that is the sum of a convex function f and an 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.

• 出版日期2016-9
• 单位西北大学