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Global Optimization in Action
Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications Pintér, János D. Series: Nonconvex Optimization and Its Applications, Vol. 6 © Kluwer Academic Publishers, Dordrecht / Boston / London, 1996. Now distributed by Springer Science and Business Media, New York. In science, engineering and economics, decision problems are frequently modeled by optimizing the value of a given (objective) function subject to (feasibility) constraints. In many cases of practical relevance - specifically, in continuous nonlinear optimization - the decision model could have multiple (local and global) optima. In such cases, it is natural to search for the globally best solution. This monograph provides a comprehensive discussion of adaptive partition (generalized branch-and-bound) strategies and stochastic search methods to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible their straightforward generalizations and extensions. The book also discusses computer-based software implementations of these global optimization strategies. A considerable part of the book is devoted to scientific and engineering applications, including systems of nonlinear equations and inequalities, data classification, aggregation of expert information, product mixture design, model fitting to data (calibration), as well as several real-world case studies in environmental systems analysis and management. The book is essentially self-contained and is based on the author's research, in cooperation (on applications) with a number of colleagues. Written for: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences. This research monograph was awarded the 2000 INFORMS Computing Society Prize, and it is available to INFORMS members with a special discount. The book is also available for course adoption at a special price: please contact us for details. Materials from this work are part of my tutorial and workshop presentations on nonlinear optimization (with a focus on algorithms, software, and applications).
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Computational Global Optimization in Nonlinear Systems An Interactive Tutorial Pintér, János D. © Lionheart Publishing, Atlanta, GA, 2001. This tutorial is a concise, admittedly "easy-going" and practical introduction to the subject of global optimization. A special emphasis is placed upon computational aspects. First, a brief review of frequently used (theoretically) exact and heuristic global optimization models and methods is provided, then software development and performance testing issues are highlighted. This is followed by a discussion of several illustrative examples which are based on real-world applications. The LGO integrated modeling and solver system embedded in a model development environment (IDE) is introduced and used to solve these examples. The corresponding demonstration program files are also made available. Please note that the LGO global/local nonlinear solver suite has been further developed significantly since the publication of this tutorial, see the current software implementations. Written for: Researchers and practitioners (perhaps without an in-depth mathematical / ORMS background) in consulting organizations and industry. Materials from this work are also part of my tutorial and workshop presentations on nonlinear optimization. |
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Global Optimization Scientific and Engineering Case Studies Pintér, János D. (Editor) Series: Nonconvex Optimization and Its Applications, Vol. 85 © Springer Science and Business Media, New York, 2006. Optimization models based on a nonlinear systems description often possess multiple local optima. The objective of global optimization (GO) is to find the best possible solution of multiextremal problems. This volume illustrates the applicability of GO modeling techniques and solution strategies to real-world problems. The contributed chapters cover a broad range of applications from agroecosystem management, assembly line design, bioinformatics, biophysics, black box systems optimization, cellular mobile network design, chemical process optimization, chemical product design, composite structure design, computational modeling of atomic and molecular structures, controller design for induction motors, electrical engineering design, feeding strategies in animal husbandry, the inverse position problem in kinematics, laser design, learning in neural nets, mechanical engineering design, numerical solution of equations, radiotherapy planning, robot design, and satellite data analysis. The solution strategies discussed encompass a range of practically viable methods, including both theoretically rigorous and heuristic approaches. Written for: Researchers and practitioners in academia, research and consulting organizations, and industry. |
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Global Optimization with Maple An Introduction with Illustrative Examples Pintér, János D. Published and distributed by Pintér Consulting Services Inc., Halifax, NS, Canada and Maplesoft, a division of Waterloo Maple Inc., Waterloo, ON, Canada © Pintér Consulting Services Inc., 2006. This (approximately 150-page when printed) electronic book presents Maple as an advanced model development and optimization environment. A special emphasis is placed on solving multi-extremal models, using the Global Optimization Toolbox for Maple. Following a brief topical introduction, an extensive collection of detailed numerical examples and illustrative case studies is presented. The book is available in the form of a fully functional (interactive and readily modifiable), printable Maple worksheet, and/or as a set of hyper-linked Maple worksheets. This "live" e-book works with Maple 9.5 or above, across all supported Maple platforms. To solve the models presented in the book, the Global Optimization Toolbox is recommended, and it is used throughout the book. Readers may also like to experiment with built-in Maple optimization functionality, or perhaps with their own native Maple solvers. Written for: Practitioners, researchers, academics and students in the quantitative sciences and engineering. Materials from this work are also part of my tutorial and workshop presentations on nonlinear optimization. |
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