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Principles of optimal design. Modeling and computation. 2nd ed. (English) Zbl 0962.90002

Cambridge: Cambridge University Press. xxii, 390 p. (2000).
This book aims to provide a thorough and comprensive guide to the complexities of engineering design using optimization and other related models. It is intended primarily as a graduate book for engineers, but it should be useful also for proffesors of optimization and numerical analysis.
The book is divided into 8 chapters of roughly equal length. They cover optimization models, model construction and model boundness, integer and parametric-discrete optima, local computation boundary and principles-practice. Structurally a system is a ’collection of entities’ in which a known input is transformed to an output. The first chapter is devoted to the discussion of mathematical modeling and its links with design optimization for decision making. The authors discuss different aspects of optimization model construction and the determination of optimal design configurations. A brief description of the modelation processes present in the development of engineerign systems is given. In the second chapter various general methods for organizing the data generated by the system’s outputs (regression curve fitting, artificial intelligence methods and kringing) are presented. The discussion on regression lacks of references to \(L_1\) Norm, Non-parametric and other alternative optimization approaches different from the Least Square criterium . The computational aspects of the methods are analyzed.
The lecture of Chapter 3 is refreshing and some fundamental subjects on model boundeness are studied in detail. The relation between the commonly used concepts of optima and boundness are carefully identifyed. Constrained and unconstrained optimization models constitute the maint topics of the chapter. The modelation process is discussed and some systems are modeled for illustrating purpouses. Chapter 4 is primarily concerned with the derivation of interior optima. Classical numerical methods such as Newton, Modified Newton, Gradient and Cholesky are presented. Anyone who wants to obtain a quick idea on Constrained Optimization as an extension of the Unconstrained problem will find Chapter 5 very helpful. It shows concisely the subject of Linear Programming. The basic algorithm is given and 15 examples are used in the discussion. A similar role for Nonlinear Programming is played by Chapter 7. Chapter 6 discusses the use of monotonicity analyis in model reduction and case decomposition. Procedures from Parametric Optimization and Discrete Optimization are presented and appropriately discussed. Numerical aspects of them are analyzed and 6 examples are used in the discussion of the behavior of the procedures. The final chapter deals with various aspects of the optimal design problem. It addresses the dialectic relation between Principles (Theory) and Practice (Real life problems) which includes a list of 12 useful software packages and 8 important internet web sites.
More than 100 exercises are proposed and each chapter ends with a summary and historical notes.
The book teaches a lot about the optimization needed for engineering design and which models engineers use for optimizimg their designs.

MSC:

90-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C05 Linear programming
90C30 Nonlinear programming
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