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On Gap Functions and Duality of Variational Inequality Problems

✍ Scribed by G.Y Chen; C.J Goh; X.Q Yang

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
219 KB
Volume
214
Category
Article
ISSN
0022-247X

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✦ Synopsis

We extend the definition of the gap function defined by Auslender for a more general class of variational inequality problems involving some convex function. A study of the duality of the extended variational inequality problem and its dual sheds new light on the meaning of gap functions. Convexity and differentiability of the gap function are also studied and sufficient conditions are derived. We also show how the gap functions for the primal and the dual are related by dual Fenchel optimization problems.

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