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Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities

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  • In optimization problems, it is significant to study the directional derivatives and subdifferentials of objective functions. Using directional derivatives and subdifferentials of objective functions, we can establish optimality conditions, derive error bound properties, and propose optimal algorithms. In this paper, the upper and lower estimates for the Clarke directional derivatives of a class of marginal functions are established. Employing this result, we obtain the exact formulations of the Clarke directional derivatives of the regularized gap functions for nonsmooth quasi-variational inequalities.
    Mathematics Subject Classification: Primary: 90C33; Secondary: 49J52, 49J53, 90C25.

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