Gâteaux differentiability of the dual gap function of a variational inequality

Zili Wu, Soon Yi Wu*

*Corresponding author for this work

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Abstract

In terms of the mapping involved in a variational inequality, we characterize the Gâteaux 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 Gâteaux 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.

Original languageEnglish
Pages (from-to)328-344
Number of pages17
JournalEuropean Journal of Operational Research
Volume190
Issue number2
DOIs
Publication statusPublished - 16 Oct 2008
Externally publishedYes

Keywords

  • Directional derivative
  • Dual gap function
  • Gâteaux differentiability
  • Variational inequality
  • Weak sharpness

Cite this

Wu, Z., & Wu, S. Y. (2008). Gâteaux differentiability of the dual gap function of a variational inequality. European Journal of Operational Research, 190(2), 328-344. https://doi.org/10.1016/j.ejor.2007.06.024