摘要
本文给出了一个新的求解非凸规划问题的同伦方法,称为动边界同伦方程,并在较弱的条件下,证明了同伦路径的存在性和大范围收敛性．与已有的拟法锥条件、伪锥条件下的修正组合同伦方法相比,同伦构造更容易,并且不要求初始点是可行集的内点,因此动边界组合同伦方法比修正组合同伦方法及弱法锥条件下的组合同伦内点法和凝聚约束同伦方法更便于应用．
A new homotopy method, called boundary moving combined homotopy method, for solving nonconvex programming is given, and the existence and convergence of the homotopy path is proved under some weak conditions. The homotopy is easier to be constructed than the modified combined homotopy under quasi-normal cone condition and pseudo-cone condition. Moreover, it need not to choose the start point inside the interior part of the feasible set, so the method is more convenient to be implemented than the modified combined homotopy method as well as the combined homotopy interior point method and the aggregate constraint homotopy method under weak normal cone condition.
基金
国家自然科学基金(10671029)
关键词
非线性规划
非凸规划
同伦算法
Nonlinear programming
nonconvex programming
homotopy method
