Global Optimization

This self-contained monograph presents a new stochastic approach to global optimization problems arising in a variety of disciplines including mathematics, operations research, engineering, and economics. The volume deals with constrained and unconstrained problems and puts a special emphasis on large scale problems. It also introduces a new unified concept for unconstrained, constrained, vector, and stochastic global optimization problems. All methods presented are illustrated by various examples. Practical numerical algorithms are given and analyzed in detail.

The topics presented include the randomized curve of steepest descent, the randomized curve of dominated points, the semi-implicit Euler method, the penalty approach, and active set strategies. The optimal decoding of block codes in digital communications is worked out as a case study and shows the potential and high practical relevance of this new approach.

Global Optimization: A Stochastic Approach is an elegant account of a refined theory, suitable for researchers and graduate students interested in global optimization and its applications.

• Large scale optimization
• Predictor Corrector Method
• Probability Theory on Manifolds
• Randomized algorithms
• Unconstrained Global Optimization
• Vector Optimization

From the reviews:

“This book includes a well-written and structured state-of-the-art survey, which gives the interested reader, both practitioner and researcher, essential information on what is necessary for global optimization. The book also provides information on recent and ongoing scientific investigations worldwide; thus, it invites readers to do their own scientific studies. … We believe that both today’s and future generations of students, teachers, researchers, and industry representatives could benefit from this book.” (Miray Hanım (Aslan) Yıldırım and Gerhard-Wilhelm Weber, Interfaces, Vol. 44 (1), January-February, 2014)

“Introducing stochastic methods, the author presents an elegant and widely applicable new approach to global optimization, constrained or unconstrained, scalar or vector, with special emphasis on large scale problems. … Practical numerical methods are discussed in detail. Numerous explicit examples and problems are given. … Due to three appendices summarizing the tools from probability, the book is self-contained … for the reader familiar with some basics of initial value problems and classical local optimization.” (Heinrich Hering, Zentralblatt MATH, Vol. 1262, 2013)

• , Fak. Elektro- und Informationstechnik, Universität der Bundeswehr München, Neubiberg, Germany

  Stefan Schäffler

Policies and ethics