Nonlinear Multiobjective Optimization

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Springer Science & Business Media, 1999 - Business & Economics - 298 pages
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Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization.
Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980.
Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well.
This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.
  

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The explanation of pareto optimality in pages 10 to 15 are worth reading by new researhers to have a good understanding of the fundamentals.

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Page 289 - M. Meika, An Integration of Efficiency Projections into the Geoffrion Approach for Multiobjective Linear Programming, European Journal of Operational Research 16, No.
Page 269 - Theory and Decision Library, Series B: Mathematical and Statistical Methods, D. Reidel Publishing Company, 1987. Kaliszewski I., A Characterization of Properly Efficient Solutions by an Augmented Tchebycheff Norm, Bulletin of the Polish Academy of Sciences - Technical Sciences 33, No. 7-8 (1985), 415-420. , Norm Scalarization and Proper Efficiency in Vector Optimization, Foundations of Control Engineering 11, No.
Page 283 - ... Nonpreemptive Multi-Objective Programming: Relationships and Counterexamples, Journal of Optimization Theory and Applications 39, No. 2 (1983), 173-186. Shin WS, A. Ravindran, Interactive Multiple Objective Optimization: Survey I - Continuous Case, Computers and Operations Research 18, No. 1 (1991), 97-114. , A Comparative Study of Interactive Tradeoff Cutting Plane Methods for MOMP, European Journal of Operational Research 56, No.

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