This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.

The Traffic Assignment Problem: Models and Methods (Dover Books on Mathematics)

Engineering & Transportation

Patriksson, Michael

Transportation

Dover Publications

This text provides a basis for the analysis of optimization models and candidate optimal solutions, especially for continuous optimization models. The treatment focuses on the analysis and algebra that underlie the workings of convexity and duality and necessary/sufficient local/global optimality conditions for unconstrained and constrained optimization problems. Newly revised and expanded third edition.

An Introduction to Continuous Optimization: Foundations and Fundamental Algorithms, Third Edition (Dover Books on Mathematics)

Science & Math

Andreasson, Niclas

Evgrafov, Anton

Mathematics

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Nonlinear Programming and Variational Inequality Problems: A Unified Approach (Applied Optimization, 23)

Business & Money

Management & Leadership

Springer

Nonlinear Programming and Variational Inequality Problems: A Unified Approach (Applied Optimization)

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