Spectral Estimation Via Convex Programming

There are many concrete optimization problems that can be reduced to minimizing a convex objective function over an infinite-dimensional convex cone subject to a finite number of equality (or inequality) constraints. Typically the cone fails to have a nonempty interior, and so classical constraint conditions do not apply. Two such types of problems concern constrained spline interpolation and spectral estimation. An earlier treatment of such problems in the context of statistical information theory can be traced back to the work of Ben-Tal and Charnes [1], which in turn extended the finite-dimensional results of Charnes and Cooper [7].