Quasi interiors,lagrange multipliers,andL p spectral estimation with lattice bounds

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 [, ].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.