Boundary Moving Combined Homotopy Method for Nonconvex Nonlinear Programming

Abstract:

      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.