Author | Mockus, Jonas. author |
---|---|

Title | Bayesian Approach to Global Optimization [electronic resource] : Theory and Applications / by Jonas Mockus |

Imprint | Dordrecht : Springer Netherlands, 1989 |

Connect to | http://dx.doi.org/10.1007/978-94-009-0909-0 |

Descript | 270 p. online resource |

CONTENT

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 Tรถrn -- 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

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