中文摘要：

长期以来，人们一直利用同伦方法来计算凸集上的Brouwer不动点问题．对于非凸集上的不动点问题，一直没有相应的结果．直到1996年，于波等人才提出了同伦内点方法来解决该类问题．于波等人进一步把凝聚函数的思想引入到同伦内点方法，从而提出了凝聚约束同伦方法（记作ACH方法）．本文对ACH方法进行改进并使得改进的方法能够求解更一般的非凸集上的不动点问题，而且改进的方法还能够扩大初始点的选择范围，并且保留了ACH方法的原有优点，即大大降低了不动点问题的求解规模，从而提高了计算效率．

英文摘要：

Since 1976, homotopy method has been used to solve fixed point problem in convex set. However, there has been hardly any result for computing fixed point problem in general nonconvex subsets. Until 1996, Yu Bo et. al proposed a homotopy interior point method to complete this work. Moreover, they introduce the idea of the aggregate function for the homotopy interior point method and hence proposed an aggregate constraint homotopy method （denoted as ACH method）. In this paper, the authors modify the ACH method and use the modified one to solve fixed point problem in a broader class of nonconvex subsets. And the modified ACH method also enlarges the choice scope of initial points. At last, this method still possesses the main advantage of the ACH method, i.e. reduces the scale of the fixed point problem largely and thus improves the computational efficiency.