Variational inequalities in vector optimization

Crespi Giovanni P., Ginchev Ivan () and Rocca Matteo ()
Additional contact information
Crespi Giovanni P.: Department of Economics, University of Insubria, Italy
Ginchev Ivan: Department of Mathematics Varna, Bulgaria
Rocca Matteo: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: 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 [8]. 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 [4].

Pages: 18 pages
Date: 2004-10
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf04020

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