Gateaux differentiability of the dual gap function of a variational inequality

Zili Wu and Soon-Yi Wu

European Journal of Operational Research, 2008, vol. 190, issue 2, 328-344

Abstract: In terms of the mapping involved in a variational inequality, we characterize the Gí¢teaux differentiability of the dual gap function G and present several sufficient conditions for its directional derivative expression, including one weaker than that of Danskin [J.M. Danskin, The theory of max-min, with applications, SIAM Journal on Applied Mathematics 14 (1966) 641-664]. When the solution set of a variational inequality problem is contained in that of its dual problem, the Gí¢teaux differentiability of G on the latter turns out to be equivalent to the conditions appearing in the authors' recent results about the weakly sharp solutions of the variational inequality problem.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:190:y:2008:i:2:p:328-344

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