A second-order method for convex 1-regularized optimization with active-set prediction
A second-order method for convex 1-regularized optimization with active-set prediction
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DOI：
10.1080/10556788.2016.1138222
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发表时间：
2015-05
影响因子：
2.2
通讯作者：
N. Keskar;J. Nocedal;Figen Öztoprak;A. Wächter
中科院分区：
文献类型：
--
作者：
N. Keskar;J. Nocedal;Figen Öztoprak;A. Wächter
我们描述了一种有效集方法，用于最小化目标函数φ，该目标函数是光滑凸函数f和正则化项之和。该方法的一个显着特点是，其中活动集识别和二阶子空间最小化步骤集成的方式，联合收割机的预测能力的两种方法。在每次迭代中，该算法选择一个自由和固定变量的候选集，执行（不精确的）子空间阶段，然后评估新的活动集的质量。如果它被判断为不可接受，则自由变量的集合被限制，并进行新的活动集预测。我们建立了我们的方法的Lipschitz连续性和强凸性的假设下，f的全局收敛性，并比较新的方法对国家的最先进的代码。
We describe an active-set method for the minimization of an objective function φ that is the sum of a smooth convex function f and an -regularization term. A distinctive feature of the method is the way in which active-set identification and second-order subspace minimization steps are integrated to combine the predictive power of the two approaches. At every iteration, the algorithm selects a candidate set of free and fixed variables, performs an (inexact) subspace phase, and then assesses the quality of the new active set. If it is not judged to be acceptable, then the set of free variables is restricted and a new active-set prediction is made. We establish global convergence for our approach under the assumptions of Lipschitz-continuity and strong-convexity of f, and compare the new method against state-of-the-art codes.