Pseudomonotone$${_{ast}}$$ maps and the cutting plane property |
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Authors: | Nicolas Hadjisavvas Siegfried Schaible |
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Affiliation: | (1) Department of Product and Systems Design Engineering, University of the Aegean, 84100 Hermoupolis, Syros, Greece;(2) A.G. Anderson Graduate School of Management, University of California, Riverside, CA 92512, USA |
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Abstract: | Pseudomonotone maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity of the map implies the “maximum principle sufficiency” and, in fact, is equivalent to it in a sense. We then present two applications of pseudomonotone maps. First we show that pseudomonotone maps can be used instead of the much more restricted class of pseudomonotone+ maps in a cutting plane method. Finally, an application to a proximal point method is given. |
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Keywords: | Variational inequality Pseudomonotone IEq6" > /content/k45002jg41k67gt5/10898_2008_9335_Article_IEq6.gif" alt=" $${_{ast}}$$" align=" middle" border=" 0" > map Cutting plane method Minimum principle sufficiency Maximum principle sufficiency |
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