Well-posed vector equilibrium problems

We introduce and study two notions of well-posedness for vector equilibrium\r\nproblems in topological vector spaces; they arise from the well-posedness\r\nconcepts previously introduced by the same authors in the scalar case, and provide\r\nan extension of similar definitions for vector optimization problems. The first notion\r\nis linked to the behaviour of suitable maximizing sequences, while the second one is\r\ndefined in terms of Hausdorff convergence of the map of approximate solutions. In\r\nthis paper we compare them, and, in a concave setting, we give sufficient conditions\r\non the data in order to guarantee well-posedness. Our results extend similar results\r\nestablished for vector optimization problems known in the literature.