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AN EXTENDED GAUSS-SEIDEL METHOD FOR MULTI-VALUED MIXED COMPLEMENTARITY PROBLEMS

E. Allevi, A. Gnudi and I. V. Konnov
Taiwanese Journal of Mathematics
Vol. 13, No. 2B, SPECIAL ISSUE for 9th International Symposium on Generalized Convexity/Monotonicity (April 2009), pp. 777-788
Stable URL: http://www.jstor.org/stable/43834762
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
AN EXTENDED GAUSS-SEIDEL METHOD FOR MULTI-VALUED MIXED COMPLEMENTARITY PROBLEMS
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Abstract

The complementarity problem (CP) is one of the basic topics in nonlinear analysis. Since the constraint set of CP is a convex cone or a cone segment, weak order monotonicity properties can be utilized for its analysis instead of the usual norm monotonicity ones. Such nonlinear CPs with order monotonicity properties have a great number of applications, especially in economics and mathematical physics. Most solution methods were developed for the single-valued case, but this assumption seems too restrictive in many applications. In the paper, we consider extended concepts of multivalued Z-mappings and examine a class of generalized mixed complementarity problems (MCPs) with box constraints, whose cost mapping is a general composition of multi-valued mappings possessing Z type properties. We develop a Gauss-Seidel algorithm for these MCPs. Some examples of computational experiments are also given.

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