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Global error bounds for convex multifunctions and applications. (English) Zbl 0977.90054
Summary: We give some results on the existence of global error bounds for convex multifunctions between normed linear spaces (until the present, only some results on local error bounds have been known in this general setting). As applications we abtain, among others, improvements of a theorem of Robinson on global error bounds for convex inequalities, of a result of Luo and Tseng on uniform boundedness of the Hoffman constants for linear inequalities and equalities, and of Lotov’s result on pointwise Lipschitz continuity of the solution sets of linear inequalities, with respect to data perturbations.

MSC:
90C31Sensitivity, stability, parametric optimization
49J52Nonsmooth analysis (other weak concepts of optimality)
49K40Sensitivity, stability, well-posedness of optimal solutions