The role of duality in optimization problems involving entropy functionals with applications to information theory

We consider infinite-dimensional optimization problems involving entropy-type functionals in the objective function as well as as in the constraints. A duality theory is developed for such problems and applied to the reliability rate function problem in information theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45233/1/10957_2004_Article_BF00939682.pd

A dual approach to multidimensional L_p spectral estimation problems

A complete duality theory is presented for the multidimensional L_p spectral estimation problem. The authors use a new constraint qualification (BWCQ) for infinite-dimensional convex programs with linear type constraints recently introduced in [Borwein and Wolkowicz, Math. Programming, 35 (1986), pp. 83-96]. This allows direct derivation of the explicit optimal solution of the problem as presented in [Goodrich and Steinhardt, SIAM J. Appl. Math., 46 (1986), pp. 417-426], and establishment of the existence of a simple and computationally tractable unconstrained Lagrangian dual problem. Moreover, the results illustrate that (BWCQ) is more appropriate to spectral estimation problems than the traditional Slater condition (which may only be applied after transformation of the problem into an L_p space [Goodrich and Steinhardt, op. cit.] and which therefore yields only necessary conditions)