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

✍ Scribed by Daniel Scholz (auth.)

• Publisher: Springer-Verlag New York
• Year: 2012
• Tongue: English
• Leaves: 153
• Series: Springer Optimization and Its Applications 63
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xiv
Principles and basic concepts....Pages 1-14
The geometric branch-and-bound algorithm....Pages 15-24
Bounding operations....Pages 25-57
Extension for multicriteria problems....Pages 59-71
Multicriteria discarding tests....Pages 73-82
Extension for mixed combinatorial problems....Pages 83-96
The circle detection problem....Pages 97-108
Integrated scheduling and location problems....Pages 109-116
The median line problem....Pages 117-127
Summary and discussion....Pages 129-132
Back Matter....Pages 133-142

✦ Subjects

Optimization; Operations Research, Management Science; Computational Science and Engineering; Algorithms