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Zbl 0734.90098
Harker, Patrick T.; Pang, Jong-Shi
Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. (English)
[J] Math. Program., Ser. B 48, No.2, 161-220 (1990). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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 modelling, 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.

MSC 2000:: *90C33 Complementarity problems
90-02 Research monographs (optimization)
49J40 Variational methods including variational inequalities
91B50 Equilibrium in economics
91D25 Spatial models
91A10 Noncooperative games

Keywords: fixed points; Walrasian equilibrium; traffic assignment; network equilibrium; spatial price equilibrium; Nash equilibrium; finite- dimensional variational inequality; complementarity; transportation planning; energy modelling; state-of-the-art review

Cited in: Zbl 1042.90048

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Zentralblatt MATH Berlin [Germany]