Deterministic Global Optimization: Geometric Branch-and-bound Methods and their Applications

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Springer Science & Business Media, Nov 6, 2011 - Mathematics - 142 pages

This monograph deals with a general class of solution approaches in deterministic global optimization, namely the geometric branch-and-bound methods which are popular algorithms, for instance, in Lipschitzian optimization, d.c. programming, and interval analysis.It also introduces a new concept for the rate of convergence and analyzes several bounding operations reported in the literature, from the theoretical as well as from the empirical point of view. Furthermore, extensions of the prototype algorithm for multicriteria global optimization problems as well as mixed combinatorial optimization problems are considered. Numerical examples based on facility location problems support the theory. Applications of geometric branch-and-bound methods, namely the circle detection problem in image processing, the integrated scheduling and location makespan problem, and the median line location problem in the three-dimensional space are also presented.

The book is intended for both researchers and students in the areas of mathematics, operations research, engineering, and computer science.

 

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Contents

Chapter 1 Principles and basic concepts
1
Chapter 2 The geometric branchandbound algorithm
15
Chapter 3 Bounding operations
25
Chapter 4 Extension for multicriteria problems
59
Chapter 5 Multicriteria discarding tests
72
Chapter 6 Extension for mixed combinatorial problems
83
Chapter 7 The circle detection problem
97
Chapter 8 Integrated scheduling and location problems
109
Chapter 9 The median line problem
117
Chapter 10 Summary and discussion
129
References
133
Index
140
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