Gâteaux differentiability of the dual gap function of a variational inequality |
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Authors: | Zili Wu Soon-Yi Wu |
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Affiliation: | Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan |
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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. |
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Keywords: | Variational inequality Dual gap function Gâ teaux differentiability Directional derivative Weak sharpness |
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