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: R n → R m 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
CRESPI, GIOVANNI PAOLO;IVANOV, IVAN GINCHEV;ROCCA, MATTEO
2010-01-01
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: R n → R m 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]
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