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

Haisen Zhang

doi:10.3934/mcrf.2014.4.365

Article Contents

2014, Volume 4, Issue 3: 365-379. Doi: 10.3934/mcrf.2014.4.365

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

Haisen Zhang^1,

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

Received: July 2013

Revised: November 2013

Published: September 2014

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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.

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Mathematics Subject Classification: Primary: 90C33; Secondary: 49J52, 49J53, 90C25.

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