QUASI INTERIORS, LAGRANGE MULTIPLIERS, AND LP SPECTRAL ESTIMATION WITH LATTICE BOUNDS

Lagrange multipliers useful in characterizations of solutions to spect ral estimation problems are proved to exist in the absence of Slater's condition provided a new constraint involving the quasi-relative inte rior holds. We also discuss the quasi interior and its relation to oth er generalizations of the interior of a convex set and relationships b etween various constraint qualifications. Finally, we characterize sol utions to the L(p) spectral estimation problem with the added constrai nt that the feasible vectors lie in a measurable strip [alpha, beta].