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Mathematical Control and Related Fields (MCRF)
 

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

Pages: 365 - 379, Volume 4, Issue 3, September 2014      doi:10.3934/mcrf.2014.4.365

 
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Haisen Zhang - School of Mathematics, Sichuan University, 610064, Chengdu, China (email)

Abstract: 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.

Keywords:  Nonsmooth quasi-variational inequality, regularized gap function, Clarke directional derivative.
Mathematics Subject Classification:  Primary: 90C33; Secondary: 49J52, 49J53, 90C25.

Received: July 2013;      Revised: November 2013;      Available Online: April 2014.

 References