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Variational Inequality and Complementarity Problem

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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

Variational inequality and complementarity have much in common, but there has been little direct contact between the researchers of these two related fields ofmathematical sciences. Several problems arising from fluid mechanics, solid mechanics, structural engineering, mathematical physics, geometry, mathematical programming, and so on have the formulation of a variational inequality or complementarity problem. People working in applied mathematics mostly deal with the infinitedimensional case and they deal with variational inequality whereas people working in operations research mostly deal with the finite-dimensional problem and they use the complementarity problem. Variational inequality is a formulation for solving the problem where we have to optimize a functional. The theory is derived by using the techniques of nonlinear functional analysis such as fixed point theory and the theory of monotone operators, among others.

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Authors and Affiliations

  1. Department of Mathematics, IIT Kharagpur, India

    Sudarsan Nanda

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  1. Sudarsan Nanda
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Correspondence to Sudarsan Nanda .

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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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Nanda, S. (2011). Variational Inequality and Complementarity Problem. 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_4

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