Bayesian approach to global optimization and application to multiobjective and constrained problems
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In this paper, the Bayesian methods of global optimization are considered. They provide the minimal expected deviation from the global minimum. It is shown that, using the Bayesian methods, the asymptotic density of calculations of the objective function is much greater around the point of global minimum. The relation of this density to the parameters of the method and to the function is defined.
Algorithms are described which apply the Bayesian methods to problems with linear and nonlinear constraints. The Bayesian approach to global multiobjective optimization is defined. Interactive procedures and reduction of multidimensional data in the case of global optimization are discussed.
- Smale, S.,The Problem of the Average Speed of the Simplex Method, Proceedings of the 11th Symposium on Mathematical Programming, Bonn, Germany, pp. 530–539, 1982.
- Kirkpatrick, S., Gelatt, C. D., Vecchi, M. P. (1983) Optimization by Simulated Annealing. Science 220: pp. 611-680
- Mockus, J. B.,On the Bayesian Search of the Extremum, Automatika i Vychislitel'naya Technika, No. 3, pp. 53–62, 1972.
- Mockus, J. B.,The Bayesian Approach to Global Optimization, Proceedings of the Indian Statistical Institute Golden Jubilee Conference on Statistics: Applications and New Directions, Calcutta, India, pp. 405–430, 1981.
- Mockus, L. J.,Package of Applied Programs for Global Optimization, Proceedings of the 1986 Conference on Mathematical and Computer Simulation in Microelectronics, Vilnius, Lithuania, USSR, 1987.
- Barbee, H. C. P., Boender, C. G. E., Rinnoy Kan, A. H. G., Scheffer, C. L., Smith, R. I., Telgen, J. (1987) Hit-and-Run Algorithm for the Identification of Nonredundant Linear Inequalities. Mathematical Programming 37: pp. 184-207
- Sobolj, I. M. (1968) Multidimensional Numerical Quadrature Formula and Haar Functions. Nauka, Moscow, USSR
- Sobolj, I. M., Statnikov, R. B. (1981) The Choice of the Optimal Parameters in Problems with Many Objective Functions. Nauka, Moscow, USSR
- Shaltenis, V. R.,The Analysis of Problems in Interactive Systems of Optimization, Proceedings of the Conference on the Application of Random Search Methods to CAD, Tallin, Estonia, USSR, 1979.
- Everitt, B. S. (1978) Graphical Techniques for Multivariate Data. Heinemann Educational Books, London, England
- Anonymous, N. N.,Minimum, Package of Applied Programs for the Interactive Solution of Multimodal Problems of Optimization, GosFAP, Vilnius, Lithuania, USSR, 1982.
- Mockus, J. B. (1989) Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht, Holland
- Bayesian approach to global optimization and application to multiobjective and constrained problems
Journal of Optimization Theory and Applications
Volume 70, Issue 1 , pp 157-172
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- Kluwer Academic Publishers-Plenum Publishers
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- Global optimization
- Bayesian approach
- multiobjective optimization
- linear and nonlinear constraints
- density of observations
- Industry Sectors