# American Institute of Mathematical Sciences

September  2014, 4(3): 365-379. doi: 10.3934/mcrf.2014.4.365

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

 1 School of Mathematics, Sichuan University, 610064, Chengdu, China

Received  July 2013 Revised  November 2013 Published  April 2014

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.
Citation: Haisen Zhang. Clarke directional derivatives of regularized gap functions for nonsmooth quasi-variational inequalities. Mathematical Control & Related Fields, 2014, 4 (3) : 365-379. doi: 10.3934/mcrf.2014.4.365
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