Principles of Optimal Design: Modeling and Computation Review

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(More customer reviews)The topic -- Optimal Design -- is difficult and treating it efficiently requires a high ratio of mathematical expressions to prose. Despite this, the authors' prose is superb. This is a very readable advanced engineering text, provided that the reader is well-versed in linear algebra. A lot of care went into the writing, the design, and the consistent use of symbols throughout. The appendix includes and extensive list of references, an author index and a subject index. One shortcoming is that no solutions are given for problems. Students would benefit from having solutions to some subset of the problems.

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This text discusses modelling for design optimization. It presents a condensed version of classical optimization theory and numerical algorithms, which it integrates with the newer ideas of monotonicity analysis and model boundedness. Careful definition of new concepts and rigorous proof of simple but important principles are followed by immediate applications. It begins with the definition of modelling and the optimization problem and outlines the limitations of this approach. The authors then move on to discuss the important but rarely emphasized concepts of boundedness checking, the idea that the parameters of every model should be verified and simplified; and monotonicity analysis, a method of determining which variables actively constrain a model. Then the discussion turns to the classical theory of differential optimization and hence to powerful numerical optimization techniques. Extensive examples and exercises aid the student and provide practice.A knowledge of differential calculus is helpful.