Relative entropy and moment problems

Tryphon T. Georgiou

doi:10.1109/CDC.2005.1582854

Relative entropy and moment problems

Tryphon T. Georgiou

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We consider the von Neumann entropy (ρ) := -trace(ρlogρ) and the Kullback-Leibler-Umegaki distance double-struk S sign (ρ∥σ) := trace(ρlogρ- ρlogρ) as regularizing functional in seeking solutions to multi-variable and multi-dimensional moment problems. We show how to obtain extrema for such functional via a suitable homotopy and how to characterize all the solutions to moment problems. The range of possible applications includes the inverse problem of describing power spectra which are consistent with second-order statistics, measurement in classical thermodynamics as well as a quantum mechanics, as well as analytic interpolation encountered in modern robust control (cf. [6], [14], [15], [16], [17]).

Original language	English (US)
Title of host publication	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Pages	4397-4403
Number of pages	7
DOIs	https://doi.org/10.1109/CDC.2005.1582854
State	Published - 2005
Event	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 - Seville, Spain Duration: Dec 12 2005 → Dec 15 2005

Publication series

Name	Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Volume	2005

Other

Other	44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Country/Territory	Spain
City	Seville
Period	12/12/05 → 12/15/05

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Georgiou, T. T. (2005). Relative entropy and moment problems. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05 (pp. 4397-4403). Article 1582854 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005). https://doi.org/10.1109/CDC.2005.1582854

Relative entropy and moment problems. / Georgiou, Tryphon T.
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05. 2005. p. 4397-4403 1582854 (Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05; Vol. 2005).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Georgiou, TT 2005, Relative entropy and moment problems. in Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05., 1582854, Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, vol. 2005, pp. 4397-4403, 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05, Seville, Spain, 12/12/05. https://doi.org/10.1109/CDC.2005.1582854

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Relative entropy and moment problems

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