Infinite-dimensional semidefinite programming: regularized determinants and self-concordant barriers

Leonid Faybusovich

We discuss possible approaches to generalizations of the semidefinite programming in a more general context of the infinite-dimensional version of the Nesterov-Nemirovsky scheme. Examples of infinite-dimensional operator domains for which there exist self-concordant barriers are presented. The key notion of the regularized determinant is used to construct self-concordant barriers.

University of Notre Dame, May, 1996