Variational inequalities in vector optimization
In this paper we investigate the links among generalized scalar variational inequalities of differential type, vector variational inequalities and vector optimization problems. The considered scalar variational inequalities are obtained through a nonlinear scalarization by means of the so called ”oriented distance” function [14, 15]. In the case of Stampacchia-type variational inequalities, the solutions of the proposed ones coincide with the solutions of the vector variational inequalities introduced by Giannessi . For Minty-type variational inequalities, analogous coincidence happens under convexity hypotheses. Furthermore, the considered variational inequalities reveal useful in filling a gap between scalar and vector variational inequalities. Namely, in the scalar case Minty variational inequalities of differential type represent a sufficient optimality condition without additional assumptions, while in the vector case the convexity hypothesis was needed. Moreover it is shown that vector functions admitting a solution of the proposed Minty variational inequality enjoy some well-posedness properties, analogously to the scalar case .
|Date of creation:||Oct 2004|
|Date of revision:|
|Contact details of provider:|| Postal: Via Ravasi 2-21100 Varese|
Web page: http://www.uninsubria.it/uninsubria/facolta/econo.html
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:ins:quaeco:qf04020. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Segreteria Dipartimento)
If references are entirely missing, you can add them using this form.