Quasi interiors, lagrange multipliers, andLp 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 theLp spectral estimation problem with the added constraint that the feasible vectors lie in a measurable strip [α, β].

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