Asymptotic analysis of a class of nonlinear penalty methods for constrained multiobjective optimization

Based on some strong nonlinear Lagrangian duality results, we propose a class of nonlinear penalty methods for a constrained multiobjective optimization problem. More specifically, we obtain the set of efficient points of a constrained multiobjective optimization problem by solving a series of unconstrained multiobjective optimization problems. Under some conditions, we prove that if a sequence of points satisfy first order necessary optimality conditions of the unconstrained multiobjective optimization problems, then this sequence of points is bounded and every limit point of this sequence also satisfies the first order necessary optimality condition of the original constrained multiobjective optimization problem.