Abstract: We used combined homotopy interior point method to solve the nonconvex programming problems of convex objective function. We proved that when the homotopy map is a regular map, the homotopy algorithm converges to a local minimum. We also proved that when the objective function is nonconvex, a local minimum point of the problem can also be obtained from the homotopy algorithm under the condition of regular homotopy map, if all K-K-T points of the nonconvex programming problem are on the bound of feasible region.

Key words: nonconvex programming, interior homotopy, local minimum