Mathematics and Its Applications

1 Global optimization and the Bayesian approach.- 1.1 What is global optimization?.- 1.2 Advantages of the Bayesian approach to global optimization.- 2 The conditions of Bayesian optimality.- 2.1 Introduction.- 2.2 Reduction to dynamic programming equations.- 2.3 The existence of a measurable solution.- 2.4 The calculation of conditional expectations.- 2.5 The one-step approximation.- 2.6 The adaptive Bayesian approach.- 3 The axiomatic non-probabilistic justification of Bayesian optimality conditions.- 3.1 Introduction.- 3.2 The linearity of the loss function.- 3.3 The existence of the unique a priori probability corresponding to subjective preferences.- 3.4 Optimal method under uncertainty.- 3.5 Nonlinear loss functions.- 4 Stochastic models.- 4.1 Introduction.- 4.2 Sufficient convergence conditions.- 4.3 The Gaussian field.- 4.4 Homogeneous Wiener field.- 4.5 A case of noisy observations.- 4.6 Estimation of parameters from dependent observations.- 5 Bayesian methods for global optimization in the Gaussian case.- 5.1 The one-step approximation.- 5.2 Adaptive models.- 5.3 Extrapolation models.- 5.4 Maximum likelihood models.- 5.5 The comparison of algorithms.- 5.6 The Bayesian approach to global optimization with linear constraints.- 5.7 The Bayesian approach to global optimization with nonlinear constraints.- 5.8 The Bayesian approach to multi-objective optimization.- 5.9 Interactive procedures and the Bayesian approach to global optimization.- 5.10 The reduction of multi-dimensional data.- 5.11 The stopping rules.- 6 The analysis of structure and the simplification of the optimization problems.- 6.1 Introduction.- 6.2 Structural characteristics and the optimization problem.- 6.3 The estimation of structural characteristics.- 6.4 The estimation of a simplification error.- 6.5 Examples of the estimates.- 7 The Bayesian approach to local optimization.- 7.1 Introduction.- 7.2 The one-dimensional Bayesian model.- 7.3 Convergence of the local Bayesian algorithm.- 7.4 Generalization of a multi-dimensional case.- 7.5 Convergence in the multi-dimensional case.- 7.6 The local Bayesian algorithm.- 7.7 Results of computer simulation.- 8 The application of Bayesian methods.- 8.1 Introduction.- 8.2 The optimization of an electricity meter.- 8.3 The optimization of vibromotors.- 8.4 The optimization of a shock-absorber.- 8.5 The optimization of a magnetic beam deflection system.- 8.6 The optimization of small aperture coupling between a rectangular waveguide and a microstrip line.- 8.7 The maximization of LSI yield by optimization of parameters of differential amplifier functional blocks.- 8.8 Optimization of technology to avoid waste in the wet-etching of printed circuit boards in iron-copper-chloride solutions.- 8.9 The optimization of pigment compounds.- 8.10 The least square estimation of electrochemical adsorption using observations of the magnitude of electrode impedance.- 8.11 Estimation of parameters of the immunological model.- 8.12 The optimization of nonstationary queuing systems.- 8.13 The analysis of structure of the Steiner problem.- 8.14 The estimation of decision making by intuition on the example of the Steiner problem.- 9 Portable FORTRAN software for global optimization.- 9.1 Introduction.- 9.2 Parameters.- 9.3 Methods available.- 9.4 Common blocks.- 9.5 The function.- 9.6 The main program.- 9.7 The example of the main program.- 9.8 Description of routines.- 9.9 BAYES1, the global Bayesian method by Mockus.- 9.10 UNT, the global method of extrapolation type by Zilinskas.- 9.11 LPMIN, the global method of uniform search by Sobolj, Shaltenis and Dzemyda.- 9.12 GLOPT, the global method of clustering type by Torn.- 9.13 MIG1, the global method of Monte Carlo (uniform random search).- 9.14 MIG2, the modified version of MIG 1.- 9.15 EXTR, the global one-dimensional method by Zilinskas.- 9.16 MIVAR4, the local method of variable metrics by Tieshis.- 9.17 REQP, the local method of recursive quadratic programming by Biggs.- 9.18 FLEXI, the local simplex method by Nelder and Mead.- 9.19 LBAYES, the local Bayesian method by Mockus.- 9.20 ANAL1, the method of analysis by structure by Shaltenis.- 9.21 Portability routines.- References.- Appendix 1 The software for global optimization for IMB/PC/XT/AT and compatibles.- Appendix 2 How the global optimization software can improve the performance of your CAD system.- Appendix 3 Machine dependent constants of portable FORTRAN.