The generalized order complementarity problem |
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Authors: | G Isac M Kostreva |
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Institution: | (1) Départment de Mathématiques, Collège Militaire Royal de Saint-Jean, Québec, Canada;(2) Department of Mathematical Sciences, Clemson University, Clemson, South Carolina |
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Abstract: | Given an ordered Banach Space (E,K) andm functionsf
1,f
2,...,f
m:EE, the generalized order complementarity problem associated with {f
i} andK is to findx
0K such thatf
i(x
0)K,i=1,...,m, and (x
0,f
1(x
0),...,f
m(x
0))=0. The problem is shown to be equivalent to several fixed-point problems and equivalent to the order complementarity problem studied by Borwein and Dempster and by Isac. Existence and uniqueness of solutions and least-element theory are shown in the spacesC(, ) andL
p(, ). For general locally convex spaces, least-element theory is derived, existence is proved, and an algorithm for computing a solution is presented. Applications to the mixed lubrication theory of fluid mechanics are described. |
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Keywords: | Complementarity ordered spaces fixed points lubrication theory |
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