Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities
Haisen Zhang · Mathematical Control and Related Fields · 2014
In optimization problems, it is significant to study the directionalderivatives and subdifferentials of objective functions. Usingdirectional derivatives and subdifferentials of objective functions,we can establish optimality conditions, derive error boundproperties, and propose optimal algorithms. In this paper, the upperand lower estimates for the Clarke directional derivatives of aclass of marginal functions are established. Employing this result,we obtain the exact formulations of the Clarke directionalderivatives of the regularized gap functions for nonsmoothquasi-variational inequalities.