An approximate Newton-type proximal method using symmetric rank-one updating formula for minimizing the nonsmooth composite functions

Z. Aminifard, S. Babaie-Kafaki
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引用次数: 1

Abstract

Founded upon the scaled memoryless symmetric rank-one updating formula, we propose an approximation of the Newton-type proximal strategy for minimizing the nonsmooth composite functions. More exactly, to approximate the inverse Hessian of the smooth part of the objective function, a symmetric rank-one matrix is employed to straightly compute the search directions for a special category of well-known functions. Convergence of the given algorithm is argued with a nonmonotone backtracking line search adjusted for the corresponding nonsmooth model. Also, its practical advantages are computationally depicted in the two well-known real-world models.
利用对称秩一更新公式求非光滑复合函数极小化的近似牛顿型近端方法
基于缩放的无记忆对称1级更新公式,提出了最小化非光滑复合函数的近似牛顿型近端策略。更精确地说,为了逼近目标函数光滑部分的逆Hessian,采用对称的秩一矩阵直接计算一类已知函数的搜索方向。通过对相应的非光滑模型进行调整的非单调回溯线搜索,论证了该算法的收敛性。此外,它的实际优势在两个众所周知的现实世界模型中被计算描述。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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