基于差分进化—单纯形混合算法求解绝对值方程*

绝对值方程Ax-｜x｜=b是一个不可微的NP-hard问题。在假设矩阵A的奇异值大于1（这里矩阵A的奇异值定义为矩阵ATA特征值的非负平方根）时, 给出了一种求解绝对值方程的新方法：差分进化—单纯形混合算法。该混合算法充分发挥了差分进化算法的群体搜索性和单纯形算法的局部细致搜索性，同时也克服了差分进化算法后期搜索效率降低和单纯形算法对初始点敏感的缺陷。数值实验表明所设计的混合算法是有效的。

Differential evolution-simplex hybrid algorithm for absolute value equations

Absolute value equations Ax-|x|=b is a non-differentiable NP-hard problem in its general form.This paper proposed a new method,called differential evolution-simplex hybrid algorithm,for solving absolute value equations under the condition that all singular values of A exceed one.The method had well combined their advantages of differential evolution algorithm and simplex method.The hybrid algorithm had sufficiently displayed the characteristics of differential evolution's group searching and simplex method'...