Abstract
Lagrange multipliers useful in characterizations of solutions to spectral estimation problems are proved to exist in the absence of Slater's condition provided a new constraint involving the quasi-relative interior holds. We also discuss the quasi interior and its relation to other generalizations of the interior of a convex set and relationships between various constraint qualifications. Finally, we characterize solutions to theL p spectral estimation problem with the added constraint that the feasible vectors lie in a measurable strip [α, β].
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Communicated by D. G. Luenberger
The authors wish to thank Jonathan M. Borwein and Adrian S. Lewis for many enlightening discussions and useful suggestions. The duality approach to the general problem inL p was suggested by J. M. Borwein.
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Limber, M.A., Goodrich, R.K. Quasi interiors, lagrange multipliers, andL p spectral estimation with lattice bounds. J Optim Theory Appl 78, 143–161 (1993). https://doi.org/10.1007/BF00940705
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DOI: https://doi.org/10.1007/BF00940705