Inexact proximal Newton methods for self-concordant functions
Inexact proximal Newton methods for self-concordant functions
复制标题
自和谐函数的不精确近端牛顿法
DOI：
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发表时间：
2016
影响因子：
1.2
通讯作者：
L. Vandenberghe
中科院分区：
文献类型：
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作者：
Jinchao Li;Martin S. Andersen;L. Vandenberghe
我们分析了用一个廉价的近似算子来最小化一个自协调函数和一个凸函数之和的近似牛顿法。当采用不精确的搜索方向时，我们给出了方法的全局和局部收敛的新结果。给出了该方法在L1正则化协方差选择中的应用，该方法对逆协差阵的稀疏模式施加了先验约束。在数值实验中，用一种加速的近邻梯度法计算近邻牛顿步长，并用多前沿算法计算具有弦稀疏模式的正定矩阵的梯度和矩阵向量积与目标光滑分量的Hessian。
We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated with an application to L1-regularized covariance selection, in which prior constraints on the sparsity pattern of the inverse covariance matrix are imposed. In the numerical experiments the proximal Newton steps are computed by an accelerated proximal gradient method, and multifrontal algorithms for positive definite matrices with chordal sparsity patterns are used to evaluate gradients and matrix-vector products with the Hessian of the smooth component of the objective.