Global Optimization in Action: Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications

by János D. Pintér

Overview

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 theauthor'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.

Product Details

ISBN-13:	9781441947512
Publisher:	Springer US
Publication date:	12/06/2010
Series:	Nonconvex Optimization and Its Applications , #6
Edition description:	Softcover reprint of hardcover 1st ed. 1996
Pages:	480
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

One Global Optimization: A Brief Review.- 1.1 General Problem Statement and Special Model Forms.- 1.2 Solution Approaches.- 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 Methods on General Convex and Star Sets.- 2.7 Partition Strategies in General Lipschitz Optimization.- Three Implementation Aspects, Algorithm Modifications and Shastic Extensions.- 3.1 Diagonally Extended Univariate Algorithms for Multidimensional Global Optimization.- 3.2 Estimation 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:Shastic Model Forms.- 3.6 Adaptive Shastic Optimization Procedures.- 3.7 Estimation of Noise-Perturbed Function Values.- Four Applications.- 4.1 Nonlinear Approximation: 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.- Afterword.- Some Further Research Perspectives.- References.

Editorial Reviews

‘Pinter's book can be recommended to each reader who needs a far-reaching survey of continuous and Lipschitz optimization. The book is distinguished by its vivid and informative style, the large number of areas that are touched, the lack of longwinded and overly sophisticated expositions, and the optimum balance between theory and practical applications.'
Optima, 51 (1996)

From the Publisher

A comprehensive treatment of a broad class of deterministic, direct (gradient-free) optimization algorithms, based on adaptive, sequential partition and search in the feasible set D. The methodology is primarily recommended for solving Lipschitzian and continuous global optimization problems, in which the lack of further analytical information realistically excludes the possibility of applying more specifically "tailored" approaches. A short discussion is also devoted to adaptive stochastic algorithms, especially popular in solving difficult "black box" global optimization problems with a (merely) continuous objective function. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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