Abstract: We proposed a homotopy interior point method for solving a class of the multiobjective programming problems in  unbounded constrained sets. Firstly, by using the Hessian matrix of the objective function, we constructed a set of unboundedness conditions, and gave a simple  example to illustrate these conditions. Secondly, we  proved the existence of the interior path connecting a given initial point and a solution point of the multiobjective programming problems. Finally, we gave the global convergence results of the homotopy interior point method.

Key words: multiobjective programming problem, homotopy interior point method, unboundedness condition