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MIETTINEN, KAISA M. 1999, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Dordrecht, The Netherlands, 298 pp., $129.95.
Nonlinear multiobjective optimization is an interesting and beautiful field of research with historical roots dating back to the origins of utility and game theory. For a nice historical view of the early days, see Stadler [1979]; for example, the notion of Pareto optimality central to any discussion of multiobjective optimization was developed by Edgeworth (1881) and the economist-sociologist Vilfredo Pareto (1896).
In the preface to Nonlinear Multiobjective Optimization, Kaisa Miettinen states, "The aim here is to provide an up-to-date, self-contained and consistent survey and review of the literature and the state-of-the-art on nonlinear (deterministic) multiobjective optimization starting with basic results." In my view, the author has succeeded admirably, and the text Nonlinear Multiobjective Optimization is a very welcome addition to the field of optimization and multicriteria decision making.
Miettinen considers the continuous, deterministic, finite-dimensional, nonlinear, multiobjective, single-decision maker as the fundamental problem, and develops the text around this case in three parts.
Part 1 concerns the theory, Part 2 concerns the methodology, and Part 3, related issues. Throughout...