An airing of the Maximum Entropy/KKT method and its use for astrophysics

Keywords: Entropy. KKT Method. MaxEnt. Non linear programming.

Abstract

In this paper, after a brief history of the Maximum Entropy Principle (MaxEnt), we will discuss its generalization in an epistemological way with the use of the KKT methodology in discrete systems. For this purpose, we we will also make a brief history of the KKT method and its use. After this exhibition, we will proceed to the joint use of MaxEnt with KKT. This has already been done in some works found in the literature, but in the particular case of Astrophysics it is a new approach from our group, which we believe to be promising.

Downloads

Download data is not yet available.

Author Biographies

Alexandre Humberto Andrei, Universidade Federal do Rio de Janeiro

Observatório do Valongo, Universidade Federal do Rio de Janeiro/ Observatório Nacional, MCTIC, Rio de Janeiro.

 

Luciano Bedin, Universidade Federal de Santa Catarina

Departamento de Matemática, Universidade Federal de Santa Catarina

 

Bruno Coelho, Campus Universitário de Santiago, Aveiro, Portugal

Instituto de Telecomunicações, Campus Universitário de Santiago, Aveiro, Portugal

,

Alexandre Lyra, Universidade Federal do Rio de Janeiro

Observatório do Valongo / Programa de Pós-Graduação em História das Ciências e das Técnicas e Epistemologia (HCTE), Universidade Federal do Rio de Janeiro

Elias Rego, Universidade Federal do Rio de Janeiro

Departamento de Matemática - Universidade Federal do Rio de Janeiro

References

ANDREI, A.; COELHO, B.; GUEDES, L.; LYRA, A. 2019, The Principle of Maximum Entropy and the Luminosity Function of Quasars, Monthly Notices of the Royal Astronomical Society, v.488, p.183-190.

ANDREI, A.; COELHO, B.; GUEDES, L.; LYRA, A. 2019, em preparação.

ANTUNES, M. e LYRA, A., O Princípio da Máxima Entropia e o Problema da Razão Insuficiente, Anais do Scientiarum História XI, Rio de Janeiro: UFRJ,2018.

CANU et al., Introduction to optimization with applications in astronomy and astrophysics, em :https://hal.archives-ouvertes.fr/hal-01346134.

JAYNES, E. T, (1957), Phys. Rev. 106, p.620;``Prior Probability'', IEEE Transations On Systems Science and Cybernetics, vol.4 sec.4 N.3 (1968); “Where do we Stand on Maximum Entropy?, Maximum Entropy Formalism Conference, Massachusetts Institute of Technology, May 2-4, (1978); "Notes on Present Status and Future Prospects." In Maximum Entropy and Bayesian Methods, edited by W. T. Grandy and L. H. Schick. Kluwer, Springer, Wyoming, USA (1990).

KUHN, H.W. AND TUCKER, A.W., 1950. Nonlinear programming, In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, Ed., pp. 481–492. Berkeley; Berkeley Symp. on Math. Statist. and Prob.Proc. Second Berkeley Symp. on Math. Statist. and Prob. (Univ. of Calif. Press, 1951), 481-492 , Nonlinear Programming.

KUHN, HAROLD W. Nonlinear programming: a historical view, Nonlinear programming (Proc. Sympos., New York, 1975) Amer. Math. Soc., Providence, R. I., 1976, pp. 1–26. SIAM-AMS Proc., Vol. IX. MR 0403674,

KARUSH, W. , 1939. Minima of Functions of Several Variables with Inequalities as Side Conditions . Dissertation, Department of Mathematics, University of Chicago. Illinois;

KJELDSEN, T. H., A Contextualized Historical Analysis of the Kuhn–Tucker Theoremin Nonlinear Programming: The Impact of World War II, In: Historia Mathematica 27 (2000), 331–361.

SHANNON, C.E., “The mathematical Theory of Communication“, Bell System Tech. J.27, 379, 623 (1948).

SHIMONY, A., The Status of the Principle of Maximum Entropy, Synthesis, v.63, p-35-53 (1985).

THIÉBAUT et YOUNG (Journ. of the Optical Soc. America A, v34, n.6, p.904 (2017)).
Published
2021-06-16
How to Cite
Andrei, A. H., Bedin, L., Coelho, B., Guedes, L., Lyra, A., Mattos, M., & Rego, E. (2021). An airing of the Maximum Entropy/KKT method and its use for astrophysics. Scientiarum Historia Magazine, 1, 9. https://doi.org/10.51919/revista_sh.v1i0.276
Section
Historicidade de Saberes Tecnocientíficos