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| Volume 6, Number 1, January 2010, pp. 39-56 | |||||||||
| Giovanni P. Crespi, Ivan Ginchev and Matteo Rocca | |||||||||
| Key words: | |||||||||
| set-valued variational inequalities, minty variational principle, generalized convexity, optimization | |||||||||
| Mathematices Subject Classification: 49J53, 49J52, 47J20 | |||||||||
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| Abstract: | |||
| It is well known that a solution of a Minty scalar variational inequality of differential type is a solution of the related optimization problem, under lower semicontinuity assumption. This relation is known as ``Minty variational principle". In the vector case, the Minty variational principle has been investigated by F. Giannessi [15] and subsequently by X. M. Yang, X. Q. Yang, K. L. Teo [22]. For a differentiable objective function f RRn→RRm it holds only for pseudoconvex functions. In this paper we extend the Minty variational principle to set-valued variational inequalities with respect to an arbitrary ordering cone and non smooth objective function. As a special case of our result we get that of [22]. | |||
| Minty variational principle for set-valued variational inequalities | ||