The homotopy interior point method for solving a class of nonlinear nonconvex programming problems

In this paper, we study the following nonlinear nonconvex programming problem (P): min f(x) s.t.g(x) ≤ 0 g(x) = (g₁(x), g₂(x), ⋯, g_m(x))^T, {1, 2, ⋯, m} Under the condition that the feasible set is bounded and connected, and has a point that the boundary is not positively linearly independent at this point, we propose the combined homotopy method to solve this problem by constructing new constraint functions 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 K-K-T point of the problem is established. Numerical examples show that this method is feasible and effective.