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We present a combined homotopy interior-point method for a general multiobjective programming problem. For solving the KKT points of the multiobjective programming problem, the homotopy equation is constructed. We prove the existence and convergence of a smooth homotopy path from almost any initial interior point to a solution of the KKT system under some basic assumptions. Copyright © 2012 X. Zhao et al.

Homotopy Interior-Point Method for a General Multiobjective Programming Problem