Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications. (English) Zbl 0734.90098

Harker, Patrick T.; Pang, Jong-Shi

Math. Program., Ser. B 48, No. 2, 161-220 (1990).

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:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90-02	Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
49J40	Variational inequalities
91B50	General equilibrium theory
91D25	Spatial models in sociology
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

Software:

PITCON

References:

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