求解对称Pareto特征值问题的下降算法
首发时间:2019-04-18
摘要:基于$NCP$函数,本文给出了一个求解对称$Pareto$特征值互补问题的一类下降方法,它的主要特点是:利用$NCP$函数作为下降方向,利用精确的线性搜索代替不精确的$Armijo$ 搜索来确定步长,从而避免了因不精确搜索导致步长过小,造成算法收敛速度极慢的问题,有效提高了算法的计算效率,并利用数值试验结果说明了该算法的有效性。
关键词: 计算数学 对称矩阵 $Pareto$特征值问题 $NCP$ 函数 下降算法
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A descent algorithm for solving symmetric Pareto eigenvalue problems
Abstract:Based on the NCP function, this paper presents a class of descent methods for solving the symmetric Pareto eigenvalue complementarity problem. Its main features are: using NCP function as the descent direction, and using the accurate linear search instead of inaccurate Armijo search to determine the step size, thus avoiding due to the inaccurate search, the step size is too small, which causes the algorithm to converge very slowly. and the computational efficiency of the algorithm is effectively improved. The numerical test results show its effectiveness.
Keywords: Computational Mathematics symmetric matrix Pareto eigenvalue problem Ncp function descent algorithm
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