Spectral Estimation Via Convex Programming
There are many concrete optimization problems that can be reduced to minimizing a convex objective function over an infinite-dimensional convex cone subject to a finite number of equality (or inequality) constraints. Typically the cone fails to have a nonempty interior, and so classical constraint conditions do not apply. Two such types of problems concern constrained spline interpolation and spectral estimation. An earlier treatment of such problems in the context of statistical information theory can be traced back to the work of Ben-Tal and Charnes , which in turn extended the finite-dimensional results of Charnes and Cooper .
KeywordsEntropy Sine Acoustics Estima Marin
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- Ben-Tal, A. and A. Chames, “A Dual Optimization Framework for Some Problems of Information Theory and Statistics,” Problems in Control and Information Theory 8 (1979), 387–401.Google Scholar
- Ben-Tal, A., J.M. Borwein, and M. Teboulle, “A Dual Approach to Multidimensional Lp Spectral Estimation Problems” (submitted).Google Scholar
- Borwein, J.M. and A. Lewis, “Infinite Dimensional Convex Programming Problems with Finite Dimensional Duals” (in preparation).Google Scholar
- Burg, J.P., Maximum Entropy Spectral Analysis, Ph.D. dissertation, Stanford University, Stanford, CA, 1975.Google Scholar
- Charms, A. and W.W. Cooper, “Constrained Kuilback—Leibler Estimation; Generalized Cobb—Douglas Balance, and Unconstrained Convex Programming,” Accademia Nationale Dei Lincei 83 (1975), 568–576.Google Scholar
- Csiszar, I., “information-Type Measures of Difference of Probability Distributions and Indirect Observations,” Studia Scientifica Mathematica Hungary 2 (1967), 299–318.Google Scholar
- Karlin, S. and W. Studden, Tchebycheff Systems with Applications in Analysis and Statistics, Interscience, New York, 1966.Google Scholar
- Rockafellar, R.T., Convex Analysis, Princeton University Press, Princeton, NJ, 1970.Google Scholar
- Rockafellar, R.T., “Integral Functionals, Normal lntegrands and Measurable Selections,” in Lecture Notes in Mathematics, Vol. 543, Springer Verlag, New York, 1976, pp. 157–207.Google Scholar