Computing Methods in Optimization Problems: Papers presented by G. Arienti, A. Colonelli Daneri, M. Auslender, E. J.

By G. Arienti, A. Colonelli Daneri, M. Auslender, E. J. Beltrami, L. F. Buchanan, A. R. Stubberud, Philippe A. Clavier, R. Cosaert, E. Gottzein, A. De Maio, G. Guardabassi, A. Locatelli, S. Rinaldi, Mark Enns, H. O. Fattorini, Jean Fave, F. Caroti Ghelli, D.

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Additional resources for Computing Methods in Optimization Problems: Papers presented at the 2nd International Conference on Computing Methods in Optimization Problems, San Remo, Italy, September 9–13, 1968

Example text

One must cope with statistics which show neither mathematical functional forms nor extend over periods of time comparable to the characteristic time periods over which business projections can be averaged. Using factual statistics, one is reduced to Monte Carlo sampling methods which lead to sets of possible chains of events, and corresponding probabilities of occurrence. The introduction a priori of the confidence level one wishes to maintain permits one to assess the results in an easily understood and meaningful manner, reduce machine run-time, take into account statistics introduced for any reason, take into account deterministic and conditional strategies and even sets of possible strategies of opponents.

It is recommended that a test be made within the program from which the proper number of samples will be chose~ CONFIDENCE LEVELS Using a computer and sampling, one obtains a set of both possible chains of events and corresponding probabilities of occurrence. The next question is: What can we do with all that rather useless mass of information? How can the conclusions be presented in a meaningful and vivid manner to a busy - 48 - executive? We recommend the introduction of confidence levels. The results of a sampling can generally be arranged in order of preference (Fig.

Minimizing a Function without Calculating Derivatives. Computer J. 10 (1967), 293-296. (11) Goldfarb, D. and L. Lapidus: A Conjugate Gradient Method for ~onlinear Programming Problems with Linear Constraints. Indust. & Eng. Chem. Fund. 7 (1968), 142-151. : Extension of Davidon's Variable Metric Method to Maximization under Linear Inequality and Equality Constraints. To appear in SIAM J. 1968. : The Gradient Projection Method for Nonlinear Programming, Part I: Linear Constraints. SIAM J. 8 - 29 - (1960), 181-217.

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