This monograph is concerned with the Bayesian approach to global optimization in the case of continuous variables. The global minimum is replaced by certain approximations in the sense of the average distance defined by \[ \int_{F}(f(x)-f(x_ 0))P(df), \] where \(f=f(x)\) is the function to be minimized, F is a family of functions f, \(x_ 0\) is the exact solution of the optimization problem and P is an a priori fixed distribution.
The approach based on this definition narrows the gap between the heuristic and mathematical methods of global optimization. The book presents efficient methods, which are based on clear mathematical assumptions.
The text is organized in the following nine chapters: 1. Global optimization and the Bayesian approach; 2. The conditions of Bayesian optimality; 3. The axiomatic non-probabilistic justification of Bayesian optimality conditions; 4. Stochastic methods; 5. Bayesian methods for global optimization in the Gaussian case; 6. The analysis of structure and the simplification of the optimization problems; 7. The Bayesian approach to local optimization; 8. The application of Bayesian methods; 9. Portable FORTRAN software for global optimization.
Some Appendixes are given at the end concerning the accompanying floppy disc. Since FORTRAN is not the best language for personal computers, a version of the software using the “C” programming language has been made. It is available on request directly from the author.
The mathematical prerequisites for reading the text include considerable knowledge of probability theory and statistics, optimization theory and numerical methods.
As a conclusion let us note that this monograph contains a complete collection of up-to-date investigations, including some results belonging to the author himself.