Taiwanese Journal of Mathematics


E. Allevi, A. Gnudi, and I. V. Konnov

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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 multi-valued 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.

Article information

Taiwanese J. Math., Volume 13, Number 2B (2009), 777-788.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 90C90: Applications of mathematical programming

mixed complementarity problem multi-valued mappings Z-mappings Gauss-Seidel algorithm


Allevi, E.; Gnudi, A.; Konnov, I. V. AN EXTENDED GAUSS-SEIDEL METHOD FOR MULTI-VALUED MIXED COMPLEMENTARITY PROBLEMS. Taiwanese J. Math. 13 (2009), no. 2B, 777--788. doi:10.11650/twjm/1500405402. https://projecteuclid.org/euclid.twjm/1500405402

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