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Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications

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Abstract

Over the past decade, the field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.

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Authors and Affiliations

  1. Decision Sciences Department, The Wharton School, University of Pennsylvania, 19104-6366, Philadelphia, PA, USA

    Patrick T. Harker

  2. Department of Mathematical Sciences, The Whiting School of Engineering, The Johns Hopkins University, 21218, Baltimore, MD, USA

    Jong-Shi Pang

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The research of this author was supported by the National Science Foundation Presidential Young Investigator Award ECE-8552773 and by the AT&T Program in Telecommunications Technology at the University of Pennsylvania.

The research of this author was supported by the National Science Foundation under grant ECS-8644098.

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Harker, P.T., Pang, JS. Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. Mathematical Programming 48, 161–220 (1990). https://doi.org/10.1007/BF01582255

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