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MSC: 90C33 90C30 65C20 65L05 Keywords:Non-convex programming Combined interior homotopy Path following algorithm Global convergence a b s t r a c tIn this paper, a new algorithm for tracing the combined homotopy path of the non-convex nonlinear programming problem is proposed. The algorithm is based on the techniques of β-cone neighborhood and a combined homotopy interior point method. The residual control criteria, which ensures that the obtained iterative points are interior points, is given by the condition that ensures the β-cone neighborhood to be included in the interior part of the feasible region. The global convergence and polynomial complexity are established under some hypotheses.