A mixed integer nonlinear programming formulation for the problem of fitting positive exponential sums to empirical data

• Autorzy: Alvarez A. , Lara H.
• Języki publikacji: EN

Abstrakty

EN

In this work we deal with exponential sum models coming from data acquisition in the empirical sciences. We present a two step approach based on Tikhonov regularization and combinatorial optimization, to obtain stable parameter estimations, which fit the data. We develop properties of the solutions, based on their optimality conditions. Some numerical experiments are shown to illustrate our approach.

Słowa kluczowe

EN

mixed integer nonlinear programming; regularization; nonlinear least squares

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 4
• Strony: 481--499
• Opis fizyczny: Bibliogr. 15 poz., wykr., tab.

Twórcy

autor

Alvarez A.

autor

Lara H.

• Universidad Nacional Abierta Área de Matemática Centro Local Lara (Barquisimeto), Venezuela,

Bibliografia

• [1] A. Bemporad, D. Mignone, MIQP.M: A Matlab function for solving Mixed Integer Quadratic Programs, Technical Report, vol. Autoo-22, Switzerland, 2001.
• [2] J. Burstein, Approximations by exponentials, their extensions and differential equations, Metric Press, Boston, 1997.
• [3] C. Chong-Yung, A Fast Maximum Likelihood Estimation and Detection Algorithm for Bernoulli-Gaussian Proccess, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-35, no. 11, November 1987.
• [4] P.C. Hansen, Regularization Tools: A Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms 6 (1994), 1–35.
• [5] P.C. Hansen, Regularization Tools Version 4.0 for Matlab 7.3, Numer. Algorithms 46 (2007), 189–194.
• [6] P.C. Hansen, The L-curve and its use in the numerical treatment of inverse problems, Adv. Comput. Bioengineering, vol. 5, 2001.
• [7] P.C. Hansen, D.P. O’Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993) 6, 1487–1503.
• [8] K. Holmström, J. Petersson, A review of the parameter estimation problem of fitting positive exponential sums to empirical data, Appl. Math. Comput. 126 (2002) 1, 31–61.
• [9] C. Lanczos, Applied Analysis, Prentice Hall, Englewood Cliffs, 272–280.
• [10] A. Mohammad-Djafari, J.F. Giovannelli, G. Demoment, J. Idier, Regularization, maximum entropy and probabilistic methods in mass spectrometry data processing problems, Internat. J. Mass Spectrometry, 215 (2002) 1–3, 175–193.
• [11] P.F. Price, A comparison of the Least-Squares and Maximum likelihood estimators for counts of radiation quanta which follow a poisson distribution, Acta Cryst. Sect. A, (1979), 3557–3560.
• [12] T. Reginska, A regularization parameter in discrete ill-posed problems, SIAM J. Sci. Comput. 17 (1996) 3, 740–749.
• [13] A. Shukla, M. Peter, L. Hoffmann, Analysis of positron lifetime spectra using quantified maximum entropy and general linear filter, Nuclear Instruments Methods Phys. Res. Sect. A 335 (1993) 1–2, 310–317.
• [14] H.S. Steyn, W.J. VanWyk, Some methods for fitting compartment models to data, Technical Report, Wetenskaplike Bydraes van die pu vir cho, Porcherstroomse Universiteit vir CHO, 1977.
• [15] W.J. Wiscombe, J.W. Evans, Exponential sum fitting of radioactive transmission function, Comput. Phys. 24 (1977) 4, 416–444.