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Gateaux differentiability of the dual gap function of a variational inequality

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  • Wu, Zili
  • Wu, Soon-Yi

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.

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  • Wu, Zili & Wu, Soon-Yi, 2008. "Gateaux differentiability of the dual gap function of a variational inequality," European Journal of Operational Research, Elsevier, vol. 190(2), pages 328-344, October.
    • Handle: RePEc:eee:ejores:v:190:y:2008:i:2:p:328-344
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    Cited by:

    1. Wu, Zili, 2018. "Characterizations of weakly sharp solutions for a variational inequality with a pseudomonotone mapping," European Journal of Operational Research, Elsevier, vol. 265(2), pages 448-453.

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