Scalarization and decomposition of vector variational inequalities governed by bifunctions |
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Authors: | Nicolae Popovici Matteo Rocca |
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Affiliation: | 1. Department of Mathematics , Babe?-Bolyai University , 1, M. Kog?lniceanu St., 400084 Cluj-Napoca , Romania popovici@math.ubbcluj.ro;3. Department of Economics , University of Insubria , 71, Monte Generoso St., 21100 Varese , Italy |
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Abstract: | In this article we study the structure of solution sets within a special class of generalized Stampacchia-type vector variational inequalities, defined by means of a bifunction which takes values in a partially ordered Euclidean space. It is shown that, similar to multicriteria optimization problems, under appropriate convexity assumptions, the (weak) solutions of these vector variational inequalities can be recovered by solving a family of weighted scalar variational inequalities. Consequently, it is deduced that the set of weak solutions can be decomposed into the union of the sets of strong solutions of all variational inequalities obtained from the original one by selecting certain components of the bifunction which governs it. |
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Keywords: | generalized vector variational inequality scalarization decomposition multicriteria optimization Pareto reducibility |
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