同伦内点方法求解一类无界非凸集合上的不动点问题

摘要

给出了求解一类无界非凸集上不动点问题的同伦内点方法.利用自映射φ(x),并结合约束函数的梯度,先构造一组无界性条件,在此基础上,给出了不动点存在性的构造性证明,得到了同伦内点方法的全局收敛性.%A homotopy interior point method was proposed to solve fixed point problems in unbounded nonconvex sets. Combining the self-mapping φ(x) with the gradients of constrained functions, we constructed a set of unbounded conditions. Based on those unbounded conditions, we gave the constructive proof of the existence of fixed points, obtaining the global convergence results of the homotopy interior point method.