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Nonlinear cost network models in transportation analysis. (English) Zbl 0607.90029

The paper is an excellent survey of the nonlinear (basically convex) cost network flow optimization problems that arise in transportation analysis. In the majority of models a user optimal principle is assumed, which states that the routes actually used are the shortest under prevailing traffic conditions and their perception by the user. The most important section of the paper deals with the network equilibrium problem. Its various formulations in terms of multicommodity flow models, or nonlinear complementarity models are followed by the discussion of the solution methods for fixed and variable demands. The panorama of solution methods includes the linear approximation approach, various gradient methods, decomposition, cutting plane method and others. The remaining sections of the paper are devoted to the problem of estimation of the origin/destination matrix of mean demands and concave cost network flow problems.
It is worth to point out the scope and the completeness of the survey, which contains a list of 122 references.
Reviewer: W.A.Molisz

MSC:

90B10 Deterministic network models in operations research
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
90C30 Nonlinear programming
90B20 Traffic problems in operations research
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