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Well-posedness of l-set optimization problem under variable order structure

The concepts of well-posedness of l-set optimization problem under variable order structure are introduced, the metric characterizations and sufficient criteria of well-posedness of a l-set optimization problem are proposed, and the equivalent relations between the well-posedness of l-set optimization problem and that of a scalarization minimization problem are established. Finally, by discussing the lower semi-continuity and convexity of gap functions of l-set convex optimization problems, their well-posedness of are investigated.