A homotopy method for getting a local minimum of constrained nonconvex programming

In this paper, a combined interior point homotopy method is used to solve constrained nonconvex programming problems. Some results for the homotopy pathway are obtained. It is known that a K–K–T point can be obtained from this homotopy method, and it proves that, when the homotopy map is a regular map, the K–K–T point must be a local minimum point on choosing a proper homotopy equation.