摘要
研究一类不可微的NP-hard的问题:Ax-|x|=b,在假设矩阵A的奇异值大于1时,给出求解绝对值方程的一种新方法.通过引入一种凝聚函数将绝对值方程进行光滑化处理,进而将求解绝对值优化问题转换为无约束优化问题,然后利用社会认知优化算法进行求解.数值试验结果表明该算法是正确的和有效的.
Absolute value equations Ax-｜x｜=bis a non-differentiable NP-hard problem in its general form.A new method for solving absolute value equations is proposed under the condition that all singular values exceed one.By using the aggregate function,absolute value equations are smoothing treatment,and then transformed into an unconstrained differentiable optimization problem.Finally,the social cognitive algorithm is applied to solve this problem.Numerical results indicate that the method is correct and effective to absolute value equations.
出处
《西安工程大学学报》
CAS
2015年第2期239-243,共5页
Journal of Xi’an Polytechnic University
基金
国家自然科学基金资助项目(11301409)
关键词
绝对值方程
社会认知算法
凝聚函数
absolute value equations social cognitive algorithm aggregate function
