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Generalized Monotone Maps and Complementarity Problems

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Topics in Nonconvex Optimization

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

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Abstract

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.

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Authors and Affiliations

  1. Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, 110 016, New Delhi, India

    S. K. Neogy

  2. Indian Statistical Institute, 203, B. T. Road, 700 108, Kolkata, India

    A. K. Das

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  1. S. K. Neogy
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  2. A. K. Das
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Correspondence to S. K. Neogy .

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Editors and Affiliations

  1. Faculty of Science, Dept. of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

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Neogy, S.K., Das, A.K. (2011). Generalized Monotone Maps and Complementarity Problems. In: Mishra, S. (eds) Topics in Nonconvex Optimization. Springer Optimization and Its Applications(), vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9640-4_2

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