Generalized Monotone Maps and Complementarity Problems

Part of the Springer Optimization and Its Applications book series (SOIA, volume 50)


In this chapter, we present some classes of generalized monotone maps and their relationship with the corresponding concepts of generalized convexity. We present results of generalized monotone maps that are used in the analysis and solution of variational inequality and complementarity problems. In addition, we obtain various characterizations and establish a connection between affine pseudomonotone mapping, affine quasimonotone mapping, positive-subdefinite matrices, generalized positive-subdefinite matrices, and the linear complementarity problem. These characterizations are useful for extending the applicability of Lemke’s algorithm for solving the linear complementarity problem.


Variational Inequality Complementarity Problem Linear Complementarity Problem Generalize Convexity Nonlinear Complementarity Problem 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Indian Statistical InstituteNew DelhiIndia
  2. 2.Indian Statistical InstituteKolkataIndia

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