A Combined Homotopy Method for Solving a Nonconvex Programming with a Class of Pseudo Cone Condition

A global convergence homotopy method for solving nonconvex programming has been introduced with weaker conditions. We give a class of pseudo cone mapping and the homotopy equation, and prove in details the existence of the smooth path from almost any given point in feasible set to a KKT point to the considered problem under some conditions. We give several preliminary numerical results. Numerical results are presented to show the effectiveness of this method.