The Combined Homotopy Method for Solving a Class of Programming Problems with a Bounded Feasible Set

In this paper, we study the following nonlinear nonconvex programming problem: in f(x);s:t:gi(x) · 0; i 2 M; M = f1; 2; ¢ ¢ ¢ ;mg: Under the condition that the feasible set is bounded and connected, but it has a point that the boundary is not regular at this point, we propose the combined homotopy method to solve this problem by constructing a new constraint function and a combined homotopy equation. The convergence of the method is proved and the existence of a smooth homotopy path from any interior point to a solution of the problem is established. Our method is very different from previous homotopy method. Numerical examples show that this method is feasible and effective.