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Stability analysis of parametric variational systems

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  • In this paper, Robinson's metric regularity of a positive order around/at some point of parametric variational systems is discussed. Under some suitable conditions, the relationships among H$\ddot{o}$lder-likeness, H$\ddot{o}$lder calmness, metric regularity of a positive order and Robinson's metric regularity of a positive order are discussed for the parametric variational systems. Then, some applications to the stabilities of the optimal value map and the solution map are studied for a parametric vector optimization problem, respectively.
    Mathematics Subject Classification: Primary: 49J53, 90C31, 49K40; Secondary: 90C29.

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