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On the calmness of a class of multifunctions. (English) Zbl 1028.49018
Summary: The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.
MSC:
49J52Nonsmooth analysis (other weak concepts of optimality)
49J53Set-valued and variational analysis
90C31Sensitivity, stability, parametric optimization
49K40Sensitivity, stability, well-posedness of optimal solutions
26E25Set-valued real functions