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Mathematics | Global Optimization in Action - Continuous and Lipschitz Optimization: Algorithms, Implementations

Global Optimization in Action

Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications

Pintér, János D.

Winner of the 2000 INFORMS Computing Society prize

1996, XXVIII, 480 p.

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In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s).
Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several 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.
Audience: 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.

Content Level » Research

Keywords » algorithm - algorithms - clustering - complex system - global optimization - model - modeling - numerical analysis - operations research - optimization - system

Related subjects » Applications - Mathematics

Table of contents 

List of figures. List of tables. Preface. Part One: Global optimization: a brief review. 1.1. General problem statement and special model forms. 1.2. Solution approaches. Part Two: Partition strategies in global optimization: the continuous and the Lipschitzian case. 2.1. An introduction to partition algorithms. 2.2. Convergence properties of adaptive partition algorithms. 2.3. Partition algorithms on intervals. 2.4. Partition algorithms on multidimensional intervals. 2.5. Simplex partition strategies. 2.6. Partition models on general convex and star sets. 2.7. Partition strategies in general Lipschitz optimization. Part Three: Implementation aspects, algorithm modifications and stochastic extensions. 3.1. Diagonally extended univariate algorithms for multidimensional global optimization. 3.2. Estimations of Lipschitzian problem characteristics in global optimization. 3.3. General Lipschitz optimization applying penalty multipliers. 3.4. An implementation of a Lipschitzian global optimization procedure. 3.5. Decision making under uncertainty: stochastic model forms. 3.6. Adaptive stochastic optimization procedures. 3.7. Estimation of noise-perturbed function values. Part Four: Applications. Introductory notes. 4.1. Nonlinear approximations: systems of equations and inequalities. 4.2. Data classification (clustering) and related problems. 4.3. Aggregation of negotiated expert opinions. 4.4. Product (mixture) design. 4.5. Globally optimized calibration of complex system models. 4.6. Calibration model versions, illustrated by examples. 4.7. Dynamic modelling of phosphorus release from sediments. 4.8. Aquifer model calibration. 4.9. Industrial wastewater management. 4.10. Multiple source river pollution management. 4.11. Lake eutrophication management. 4.12. Risk management of accidental water pollution. Some further research perspectives. References. Index.

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