A dual approach to multidimensional spectral estimation problems

Borwein, Jonathan M. and Tal, A. Ben and Teboulle, M. (1988) A dual approach to multidimensional spectral estimation problems. SIAM Journal on Control and Optimization, 26 . pp. 985-996. ISSN 0363-0129

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A complete duality theory is presented for the multidimensional Lp spectral estimation problem. The authors use a new constraint qualification (BWCQ) for infinite-dimensional convex programs with linear type constraints recently introduced in [Borwein and Wolkowicz, Math. Programming, 35 (1986), pp. 83-96]. This allows direct derivation of the explicit optimal solution of the problem as presented in [Goodrich and Steinhardt, SIAM J. Appl. Math., 46 (1986), pp. 417-426], and establishment of the existence of a simple and computationally tractable unconstrained Lagrangian dual problem. Moreover, the results illustrate that (BWCQ) is more appropriate to spectral estimation problems than the traditional Slater condition (which may only be applied after transformation of the problem into an Lp space [Goodrich and Steinhardt, op. cit.] and which therefore yields only necessary conditions).

Item Type: Article
Depositing User: Mrs Naghmana Tehseen
Date Deposited: 20 Feb 2015 16:20
Last Modified: 20 Feb 2015 16:20

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